Nanotechnology and Nanoelectronics: Materials, Devices, Measurment Techniques [1 ed.] 9783540224525, 9783540266211, 3540224521

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W. R. Fahrner (Editor) Nanotechnology and Nanoelectronics Materials, Devices, Measurement Techniques

W. R. Fahrner (Editor)

Nanotechnology and Nanoelectronics Materials, Devices, Measurement Techniques

With 218 Figures

4y Springer

Prof. Dr. W. R. Fahrner University of Hagen Chair of Electronic Devices 58084 Hagen Germany

Library of Congress Control Number: 2004109048

ISBN 3-540-22452-1 Springer Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution act under German Copyright Law. Springer is a part of Springer Science + Business Media GmbH springeronline.com © Springer-Verlag Berlin Heidelberg 2005 Printed in Germany The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Digital data supplied by editor Cover-Design: medionet AG, Berlin Printed on acid-free paper 62/3020 Rw 5 4 3 2 10

Preface

Split a human hair thirty thousand times, and you have the equivalent of a nanometer. The aim of this work is to provide an introduction into nanotechnology for the scientifically interested. However, such an enterprise requires a balance between comprehensibility and scientific accuracy. In case of doubt, preference is given to the latter. Much more than in microtechnology – whose fundamentals we assume to be known – a certain range of engineering and natural sciences are interwoven in nanotechnology. For instance, newly developed tools from mechanical engineering are essential in the production of nanoelectronic structures. Vice versa, mechanical shifts in the nanometer range demand piezoelectric-operated actuators. Therefore, special attention is given to a comprehensive presentation of the matter. In our time, it is no longer sufficient to simply explain how an electronic device operates; the materials and procedures used for its production and the measuring instruments used for its characterization are equally important. The main chapters as well as several important sections in this book end in an evaluation of future prospects. Unfortunately, this way of separating coherent description from reflection and speculation could not be strictly maintained. Sometimes, the complete description of a device calls for discussion of its inherent potential; the hasty reader in search of the general perspective is therefore advised to study this work’s technical chapters as well. Most of the contributing authors are involved in the “Nanotechnology Cooperation NRW” and would like to thank all of the members of the cooperation as well as those of the participating departments who helped with the preparation of this work. They are also grateful to Dr. H. Gabor, Dr. J. A. Weima, and Mrs. K. Meusinger for scientific contributions, fruitful discussions, technical assistance, and drawings. Furthermore, I am obliged to my son Andreas and my daughter Stefanie, whose help was essential in editing this book. Hagen, May 2004

W. R. Fahrner

Contents

Contributors...........................................................................................................XI Abbreviations ..................................................................................................... XIII

1

Historical Development (W. R. FAHRNER)...........................................1 1.1 Miniaturization of Electrical and Electronic Devices .......................1 1.2 Moore’s Law and the SIA Roadmap.................................................2

2

Quantum Mechanical Aspects ..........................................................5 2.1 General Considerations (W. R. FAHRNER)........................................5 2.2 Simulation of the Properties of Molecular Clusters (A. ULYASHIN) ..................................................................................5 2.3 Formation of the Energy Gap (A. ULYASHIN) ..................................7 2.4 Preliminary Considerations for Lithography (W. R. FAHRNER) .......8 2.5 Confinement Effects (W. R. FAHRNER) ..........................................12 2.5.1 Discreteness of Energy Levels..................................................13 2.5.2 Tunneling Currents ...................................................................14 2.6 Evaluation and Future Prospects (W. R. FAHRNER)........................14

3

Nanodefects (W. R. FAHRNER)...............................................................17 3.1 Generation and Forms of Nanodefects in Crystals..........................17 3.2 Characterization of Nanodefects in Crystals...................................18 3.3 Applications of Nanodefects in Crystals.........................................28 3.3.1 Lifetime Adjustment.................................................................28 3.3.2 Formation of Thermal Donors ..................................................30 3.3.3 Smart and Soft Cut....................................................................31 3.3.4 Light-emitting Diodes...............................................................34 3.4 Nuclear Track Nanodefects.............................................................35 3.4.1 Production of Nanodefects with Nuclear Tracks ......................35 3.4.2 Applications of Nuclear Tracks for Nanodevices .....................36 3.5 Evaluation and Future Prospects.....................................................37

4

Nanolayers (W. R. FAHRNER)..................................................................39 4.1 Production of Nanolayers ...............................................................39 4.1.1 Physical Vapor Deposition (PVD)............................................39 4.1.2 Chemical Vapor Deposition (CVD)..........................................44 4.1.3 Epitaxy......................................................................................47

VIII

Contents

4.1.4 Ion Implantation........................................................................52 4.1.5 Formation of Silicon Oxide ......................................................59 4.2 Characterization of Nanolayers.......................................................63 4.2.1 Thickness, Surface Roughness .................................................63 4.2.2 Crystallinity ..............................................................................76 4.2.3 Chemical Composition .............................................................82 4.2.4 Doping Properties .....................................................................86 4.2.5 Optical Properties .....................................................................97 4.3 Applications of Nanolayers...........................................................103 4.4 Evaluation and Future Prospects...................................................103 5

Nanoparticles (W. R. FAHRNER).............................................................107 5.1 Fabrication of Nanoparticles.........................................................107 5.1.1 Grinding with Iron Balls .........................................................107 5.1.2 Gas Condensation ...................................................................107 5.1.3 Laser Ablation ........................................................................107 5.1.4 Thermal and Ultrasonic Decomposition .................................108 5.1.5 Reduction Methods.................................................................109 5.1.6 Self-Assembly ........................................................................109 5.1.7 Low-Pressure, Low-Temperature Plasma...............................109 5.1.8 Thermal High-Speed Spraying of Oxygen/Powder/Fuel ........110 5.1.9 Atom Optics............................................................................111 5.1.10 Sol gels ...................................................................................112 5.1.11 Precipitation of Quantum Dots ...............................................113 5.1.12 Other Procedures ....................................................................114 5.2 Characterization of Nanoparticles.................................................114 5.2.1 Optical Measurements ............................................................114 5.2.2 Magnetic Measurements .........................................................115 5.2.3 Electrical Measurements.........................................................115 5.3 Applications of Nanoparticles.......................................................117 5.4 Evaluation and Future Prospects...................................................118

6

Selected Solid States with Nanocrystalline Structures .....121 6.1 Nanocrystalline Silicon (W. R. FAHRNER)....................................121 6.1.1 Production of Nanocrystalline Silicon ....................................121 6.1.2 Characterization of Nanocrystalline Silicon ...........................122 6.1.3 Applications of Nanocrystalline Silicon .................................126 6.1.4 Evaluation and Future Prospects.............................................126 6.2 Zeolites and Nanoclusters in Zeolite Host Lattices (R. JOB) ........127 6.2.1 Description of Zeolites ...........................................................127 6.2.2 Production and Characterization of Zeolites...........................128 6.2.3 Nanoclusters in Zeolite Host Lattices .....................................135 6.2.4 Applications of Zeolites and Nanoclusters in Zeolite Host Lattices...............................................................138 6.2.5 Evaluation and Future Prospects.............................................139

Contents

7

IX

Nanostructuring ..................................................................................143 7.1 Nanopolishing of Diamond (W. R. FAHRNER)..............................143 7.1.1 Procedures of Nanopolishing..................................................143 7.1.2 Characterization of the Nanopolishing ...................................144 7.1.3 Applications, Evaluation, and Future Prospects .....................147 7.2 Etching of Nanostructures (U. HILLERINGMANN) .........................150 7.2.1 State-of-the-Art.......................................................................150 7.2.2 Progressive Etching Techniques .............................................153 7.2.3 Evaluation and Future Prospects.............................................154 7.3 Lithography Procedures (U. HILLERINGMANN) ............................154 7.3.1 State-of-the-Art.......................................................................155 7.3.2 Optical Lithography................................................................155 7.3.3 Perspectives for the Optical Lithography ...............................161 7.3.4 Electron Beam Lithography....................................................164 7.3.5 Ion Beam Lithography............................................................168 7.3.6 X-Ray and Synchrotron Lithography......................................169 7.3.7 Evaluation and Future Prospects.............................................171 7.4 Focused Ion Beams (A. WIECK) ...................................................172 7.4.1 Principle and Motivation ........................................................172 7.4.2 Equipment...............................................................................173 7.4.3 Theory.....................................................................................180 7.4.4 Applications............................................................................181 7.4.5 Evaluation and Future Prospects.............................................188 7.5 Nanoimprinting (H. SCHEER)........................................................188 7.5.1 What is Nanoimprinting?........................................................188 7.5.2 Evaluation and Future Prospects.............................................194 7.6 Atomic Force Microscopy (W. R. FAHRNER) ...............................195 7.6.1 Description of the Procedure and Results ...............................195 7.6.2 Evaluation and Future Prospects.............................................195 7.7 Near-Field Optics (W. R. FAHRNER) ............................................196 7.7.1 Description of the Method and Results...................................196 7.7.2 Evaluation and Future Prospects.............................................198

8

Extension of Conventional Devices by Nanotechniques ..201 8.1 MOS Transistors (U. HILLERINGMANN, T. HORSTMANN) ............201 8.1.1 Structure and Technology.......................................................201 8.1.2 Electrical Characteristics of Sub-100 nm MOS Transistors ...204 8.1.3 Limitations of the Minimum Applicable Channel Length......207 8.1.4 Low-Temperature Behavior....................................................209 8.1.5 Evaluation and Future Prospects.............................................210 8.2 Bipolar Transistors (U. HILLERINGMANN) ....................................211 8.2.1 Structure and Technology.......................................................211 8.2.2 Evaluation and Future Prospects.............................................212

X

Contents

9

Innovative Electronic Devices Based on Nanostructures (H. C. NEITZERT) ........................................................................................213 9.1 General Properties.........................................................................213 9.2 Resonant Tunneling Diode............................................................213 9.2.1 Operating Principle and Technology ......................................213 9.2.2 Applications in High Frequency and Digital Electronic Circuits and Comparison with Competitive Devices ..............216 9.3 Quantum Cascade Laser ...............................................................219 9.3.1 Operating Principle and Structure...........................................219 9.3.2 Quantum Cascade Lasers in Sensing and Ultrafast Free Space Communication Applications.......................................224 9.4 Single Electron Transistor.............................................................225 9.4.1 Operating Principle.................................................................225 9.4.2 Technology .............................................................................227 9.4.3 Applications............................................................................229 9.5 Carbon Nanotube Devices ............................................................232 9.5.1 Structure and Technology.......................................................232 9.5.2 Carbon Nanotube Transistors .................................................234

References ...........................................................................................................239 Index....................................................................................................................261

Contributors

Prof. Dr. rer. nat. Wolfgang R. Fahrner (Editor) University of Hagen Haldenerstr. 182, 58084 Hagen, Germany Prof. Dr.-Ing. Ulrich Hilleringmann University of Paderborn Warburger Str. 100, 33098 Paderborn, Germany Dr.-Ing. John T. Horstmann University of Dortmund Emil-Figge-Str. 68, 44227 Dortmund, Germany Dr. rer. nat. habil. Reinhart Job University of Hagen Haldenerstr. 182, 58084 Hagen, Germany Prof. Dr.-Ing. Heinz-Christoph Neitzert University of Salerno Via Ponte Don Melillo 1, 84084 Fisciano (SA), Italy Prof. Dr.-Ing. Hella-Christin Scheer University of Wuppertal Rainer-Gruenter-Str. 21, 42119 Wuppertal, Germany Dr. Alexander Ulyashin University of Hagen Haldenerstr. 182, 58084 Hagen, Germany Prof. Dr. rer. nat. Andreas Dirk Wieck University of Bochum Universitätsstr. 150, NB03/58, 44780 Bochum, Germany

Abbreviations

AES AFM ASIC

Auger electron spectroscopy Atomic force microscope / microscopy Application-specific integrated circuit

BSF BZ

Back surface field Brillouin zone

CARL CCD CMOS CNT CVD CW Cz

Chemically amplified resist lithography Charge-coupled device Complementary metal–oxide–semiconductor Carbon nanotube Chemical vapor deposition Continuous wave Czochralski

DBQW DFB DLTS DOF DRAM DUV

Double-barrier quantum-well Distributed feedback (QCL) Deep level transient spectroscopy Depth of focus Dynamic random access memory Deep ultraviolet

EBIC ECL ECR EDP EEPROM EL ESR ESTOR Et EUV EUVL EXAFS

Electron beam induced current Emitter-coupled logic Electron cyclotron resonance (CVD, plasma etching) Ethylene diamine / pyrocatechol Electrically erasable programmable read-only memory Electroluminescence Electron spin resonance Electrostatic data storage Ethyl Extreme ultraviolet Extreme ultraviolet lithography Extended x-ray absorption fine-structure studies

FEA FET FIB FP FTIR FWHM

Field emitter cathode array Field effect transistor Focused ion beam Fabry-Perot Fourier transform infrared Full width at half maximum

XIV

Abbreviations

HBT HEL HEMT HIT HOMO HREM

Hetero bipolar transistor Hot-embossing lithography High electron mobility transistor Heterojunction with intrinsic thin layer Highest occupied molecular orbital High resolution electron microscope / microscopy

IC ICP IMPATT IPG IR ITO ITRS

Integrated circuit Inductively coupled plasma Impact ionization avalanche transit time In plane gate Infrared Indium–tin–oxide International technology roadmap for semiconductors

Laser LBIC LDD LED LEED LMIS LPE LSS LUMO

Light amplification by stimulated emission of radiation Light beam induced current Lightly doped drain Light-emitting diode Low energy electron diffraction Liquid metal ion source Liquid phase epitaxy Lindhardt, Scharff, Schiøtt (Researchers) Lowest unoccupied molecular orbital

M MAL MBE µCP MCT Me MEMS MIS MMIC MOCVD MODFET MOLCAO MOS MOSFET MPU MQW MWNT

Metal Mould-assisted lithography Molecular beam epitaxy Microcontact printing Mercury cadmium telluride Methyl Micro electro-mechanical system Metal–insulator–semiconductor Monolithic microwave integrated circuit Metallo-organic chemical vapor deposition Modulation-doped field-effect transistor Molecular orbitals as linear combinations of atomic orbitals Metal–oxide–semiconductor Metal–oxide–semiconductor field effect transistor Microprocessor unit Multi quantum well Multi wall nanotubes

NA NAND NDR Nd:YAG NIL NMOS NMR NOR

Numerical aperture Not and Negative differential resistance Neodymium yttrium aluminum garnet (laser) Nanoimprint lithography n-Channel metal–oxide–semiconductor (transistor) Nuclear magnetic resonance Not or

Abbreviations PADOX PDMS PE PECVD PET PL PLAD PMMA PREVAIL PTFE PVD

Pattern-dependent oxidation Polydimethylsiloxane Plasma etching Plasma-enhanced chemical vapor deposition Polyethyleneterephthalate Photoluminescence Plasma doped Polymethylmethacrylate Projection reduction exposure with variable axis immersion lenses Polytetrafluorethylene (Teflon®) Physical vapor deposition

QCL QSE QWIP

Quantum cascade laser Quantum size effect Quantum well infrared photodetector

RAM RBS RCA RF RHEED RIE RITD RTA RTBT RTD

Random access memory Rutherford backscattering spectrometry Radio Corporation of America (Company) Radio frequency Reflection high-energy electron diffraction Reactive ion etching Resonant interband tunneling diode Rapid thermal annealing Resonant tunneling bipolar transistor Resonant tunneling diode

SAM SCALPEL SCZ SEM SET SFIL SHT SIA SIMOX SIMS SL SMD SOI SOS STM SWNT

Self-assembling monolayer Scattering with angular limitation projection electron beam lithography Space charge zone Scanning electron microscopy Single electron transistor Step and flash imprint lithography Single hole transistor Semiconductor Industry Association Separation by implantation of oxygen Secondary ion mass spectroscopy Superlattice Surface-mounted device Silicon on insulator Silicon on sapphire Scanning tunneling microscope / microscopy Single wall nanotubes

TA TED TEM TEOS TFT TMAH TSI

Thermal analysis Transferred electron device Transmission electron microscopy Tetraethylorthosilicate Thin film transistor Tetramethylammonium hydroxide Top surface imaging

XV

XVI

Abbreviations

TTL TUBEFET

Transistor-transistor logic Single carbon nanotube field-effect transistor

UHV ULSI UV

Ultrahigh vacuum Ultra large scale integration Ultraviolet

VHF VLSI VMT V-PADOX VPE

Very high frequency (30–300 MHz; 10–1 m) Very large scale integration Velocity-modulated transistor Vertical pattern-dependent oxidation Vapor phase epitaxy

XOR XRD

Exclusive or X-ray diffraction

ZME

Zeolite modified electrode

1

Historical Development

1.1

Miniaturization of Electrical and Electronic Devices

At present, development in electronic devices means a race for a constant decrease in the order of dimension. The general public is well aware of the fact that we live in the age of microelectronics, an expression which is derived from the size (1 µm) of a device’s active zone, e.g., the channel length of a field effect transistor or the thickness of a gate dielectric. However, there are convincing indications that we are entering another era, namely the age of nanotechnology. The expression “nanotechnology” is again derived from the typical geometrical dimension of an electronic device, which is the nanometer and which is one billionth (109) of a meter. 30,000 nm are approximately equal to the thickness of a human hair. It is worthwhile comparing this figure with those of early electrical machines, such as a motor or a telephone with their typical dimensions of 10 cm. An example of this development is given in Fig. 1.1.

(a)

20 µm

(b)

(c) Fig. 1.1 (a) Centimeter device (SMD capacity), (b) micrometer device (transistor in an IC), and (c) nanometer device (MOS single transistor)

2

1 Historical Development

1.2

Moore’s Law and the SIA Roadmap

From the industrial point of view, it is of great interest to know which geometrical dimension can be expected in a given year, but the answer does not only concern manufacturers of process equipment. In reality, these dimensions affect almost all electrical parameters like amplification, transconductance, frequency limits, power consumption, leakage currents, etc. In fact, these data have a great effect even on the consumer. At first glance, this appears to be an impossible prediction of the future. However, when collecting these data from the past and extrapolating them into the future we find a dependency as shown in Fig. 1.2. This observation was first made by Moore in 1965, and is hence known as Moore’s law. A typical electronic device of the fifties was a single device with a dimension of 1 cm, while the age of microelectronics began in the eighties. Based on this figure, it seems encouraging to extrapolate the graph, for instance, in the year 2030 in which the nanometer era is to be expected. This investigation was further pursued by the Semiconductor Industry Association (SIA) [1]. As a result of the abovementioned ideas, predictions about the development of several device parameters have been published. A typical result is shown in Table 1.1. These predictions are not restricted to nanoelectronics alone but can also be valid for materials, methods, and systems. There are schools and institutions which are engaged in predictions of how nanotechnology will influence or even rule our lives [2]. Scenarios about acquisition of solar energy, a cure for cancer, soil detoxification, extraterrestrial contact, and genetic technology are introduced. It should be considered, though, that the basic knowledge of this second method of prediction is very limited.

Fig. 1.2

Moore’s law

1.2 Moore’s Law and the SIA Roadmap Table 1.1

Selected roadmap milestones

Year Dense lines, nm Iso. lines (MPU gates), nm DRAM memory (introduced)

1997 250 200

1999 180 140

2001 150 120

2003 130 100

2006 100 70

2012 50 35

267 M 1.07 G [1.7 G] 4.29 G 17.2 G 68.7 G 275 G

11 M 21 M 40 M 76 M 200 M chip Frequency, MHz 750 1200 1400 1600 2000 Minimum supply voltage 1.8– 1.5– 1.2– 1.2– 0.9– 2.5 Vdd, V 1.8 1.5 1.5 1.2 Max. wafer diameter, mm 200 300 300 300 300 280 400 445 560 790 DRAM chip size, mm2 (introduced) 22·22 25·32 25·34 25·36 25·40 Lithography field size, mm2 484 800 850 900 1000 Maximum wiring levels 6 6–7 7 7 7–8 Maximum mask levels 24 22 24–26 22–24 23 2080 1455 [1310] 1040 735 Density of electrical DRAM defects (introduced), 1 / m2 MPU: microprocessor unit, DRAM: dynamic random access memory

MPU: transistors per

2009 70 50

520 M 1.4 G 2500 0.6– 0.9 450 1120

3000 0.5– 0.6 450 1580

25·44 1100 8–9 26–28 520

25·52 1300 9 28 370

3

2

Quantum Mechanical Aspects

2.1

General Considerations

Physics is the classical material science which covers two extremes: on the one hand, there is atomic or molecular physics. This system consists of one or several atoms. Because of this limited number, we are dealing with sharply defined discrete energy levels. On the other side there is solid-state physics. The assumption of an infinitely extended body with high translation symmetry also makes it open to mathematical treatment. The production of clusters (molecules with 10 to 10,000 atoms) opens a new field of physics, namely the observation of a transition between both extremes. Of course, any experimental investigation must be followed by quantum mechanical descriptions which in turn demand new tools. Another application of quantum mechanics is the determination of stable molecules. The advance of nanotechnology raises hopes of constructing mechanical tools within human veins or organs for instance, valves, separation units, ion exchangers, molecular repair cells and depots for medication. A special aspect of medication depot is that both the container and the medicament itself would have to be nanosynthesized. Quantum mechanics also plays a role when the geometrical dimension is equal to or smaller than a characteristic wavelength, either the wavelength of an external radiation or the de Broglie wavelength of a particle in a bound system. An example of the first case is diffraction and for the second case, the development of discrete energy levels in a MOS inversion channel.

2.2

Simulation of the Properties of Molecular Clusters

One of the first theoretical approaches to nanotechnology has been the simulated synthesis of clusters (molecular bonding of ten to some ten thousand atoms of different elements). This approach dates back to the 1970s. In a simulation, a Hamilton operator needs to be set up. In order to do so, some reasonable arrangement of the positions of the atoms is selected prior to the simulation’s beginning. An adiabatic approach is made for the solution of the eigenvalues and eigenfunctions. In our case, this means that the electronic movement is much faster than that of the atoms. This is why the electronic system can be separated from that of the atoms and leads to an independent mathematical treatment of both systems. Because of the electronic system’s considerably higher energy, the Schrödinger equation for

6

2 Quantum Mechanical Aspects

the electrons can be calculated as a one-electron solution. The method used for the calculation is called MOLCAO (molecular orbitals as linear combinations of atomic orbitals). As can be derived from the acronym, a molecular orbital is assumed to be a linear combination of orbitals from the atomic component as is known from the theory of single atoms. The eigenvalues and coefficients are determined by diagonalization in accordance with the method of linear algebra. Then the levels, i.e., the calculated eigenenergies will be filled with electrons according to the Pauli principle. Thereafter the total energy can be calculated by multiplying the sum of the eigenenergies by the electrons in these levels. A variation calculation is performed at the end in order to obtain the minimum energy of the system. The parameter to be varied is the geometry of the atom, i.e., its bonding length and angle. The simulations are verified by application on several known properties of molecules (such as methane and silane), carbon-containing clusters (like fullerenes) and vacancy-containing clusters in silicon. This method is not only capable of predicting new stable clusters but is also more accurate in terms of delivering their geometry, energy states, and optical transitions. This is already state-of-the-art [3– 5]. Thus, no examples are given. Starting from here, a great number of simulations are being performed for industrial application like hydrogen storage in the economics of energy, the synthesis of medication in the field of medicine or the development of lubricants for automobiles. As an example, we will consider the interaction between hydrogen atoms and fullerenes (Fig. 2.1). An incomplete fullerene (a fullerene with a vacancy) is selected. If placed in a hydrogen environment (14 in the simulation), the aforesaid vacancy captures four hydrogen atoms. In conclusion, a vacancy can take at least four hydrogen atoms. It is simple to produce fullerenes with a higher number of vacancies so that a fullerene can eventually be expected to be an active

Fig. 2.1 Interaction between a fullerene (which contains a vacancy) and hydrogen. The dark-gray circles represent carbon, the light-gray ones hydrogen, and the empty circle (arrow) represents a vacancy with dangling bonds.

2.3 Formation of the Energy Gap

7

storage medium for hydrogen (please consider the fact that the investigations are not yet completed). There are two further hydrogen atoms close to the vacancy which are weakly bonded to the hydrogen atoms but can also be part of the carbon-hydrogen complex. A good number of commercial programs are available for the above-named calculations. Among these are the codes Mopac, Hyperchem, Gaussian, and Gamess, to name but a few. All of these programs require high quality computers. The selection of 14 interactive hydrogen atoms was done in view of the fact that the calculation time be kept within a reasonable limit. In other applications mechanical parts such as gears, valves, and filters are constructed by means of simulation (Fig. 2.2). These filters are meant to be employed in human veins in order to separate healthy cells from infected ones (e.g., by viruses or bacteria). Some scientists are even dreaming of replacing the passive filters by active machines (immune machines) which are capable of detecting penetrating viruses, bacteria and other intruders. Another assignment would be the reconstruction of damaged tissues and even the replacement of organs and bones. Moreover, scientists consider the self-replicating generation of the passive and active components discussed above. The combination of self-replication and medicine (especially when involving genetic engineering) opens up a further field of possibilities but at the same time provokes discussions about seriousness and objectives.

2.3

Formation of the Energy Gap

As discovered above, clusters are found somewhere in the middle between the single atom on one side and the infinitely extended solid state on the other. Therefore, it should be possible to observe the transition from discrete energy states to the energy gap of the infinitely extended solid state on the other side. The results of such calculations are presented in Figs. 2.3 and 2.4. Note that the C5H12 configuration in Fig. 2.3 is not the neopentane molecule (2,2-dimethylpropane). It is much more a C5 arrangement of five C atoms as near-

(a) Fig. 2.2

(a) Nanogear [6], (b) nanotube or nanofilter [7]

(b)

8

2 Quantum Mechanical Aspects

Fig. 2.3

Development of the diamond band gap

est neighbors which are cut out of the diamond. For the purpose of electronic saturation 12 hydrogen atoms are hung on this complex. The difference to a neopentane molecule lies in the binding lengths and angles. In the examples concerning carbon and silicon, the development of the band structure is clearly visible. In another approach the band gap of silicon is determined as a function of a typical length coordinate, say the cluster radius or the length of a wire or a disc. In Fig. 2.5, the band gap versus the reciprocal of the length is shown [8]. For a solid state, the band gap converges to its well known value of 1.12 eV. It is worthwhile comparing the above-mentioned predictions with subsequent experimental results [9]. The band gap of Sin clusters is investigated by photoelectron spectroscopy. Contrary to expectations, it is shown that almost all clusters from n = 4 to 35 have band gaps smaller than that of crystalline silicon (see Fig. 2.6). These observations are due to pair formation and surface reconstruction. Scientists are in fact interested in obtaining details which are even more specific. For example, optical properties are not only determined through the band gap but through the specific dependency of the energy bands on the wave vectors. It is a much harder theoretical and computational assignment to determine this dependency. An earlier result [10] for SiC cluster is reproduced in Fig. 2.7.

2.4

Preliminary Considerations for Lithography

An obvious effect of the quantum mechanics on the nanostructuring can be found in lithography. For readers with little experience, the lithographic method will be briefly explained with the help of Fig. 2.8.

2.4 Preliminary Considerations for Lithography

Fig. 2.4

9

Development of the Si band gap

A wafer is covered with a photoresist and a mask containing black/transparent structures is laid on top of it. If the mask is radiated with UV light, the light will be absorbed in the black areas and transmitted in the other positions. The UV light subsequently hardens the photoresist under the transparent areas so that it cannot be attacked by a chemical solution (the developer). Thus, a window is opened in the photoresist at a position in the wafer where, for instance, ion implantation will be performed. The hardened photoresist acts as a mask which protects those areas that are not intended for implantation.

10

2 Quantum Mechanical Aspects

Fig. 2.5 Energy gaps vs. confinement. The different symbols refer to different computer programs which were used in the simulation.

Fig. 2.6

Measured band gaps for silicon clusters

Up to now, a geometrical light path has been tacitly assumed i.e., an exact reproduction of the illuminated areas. However, wave optics teaches us that this not true [11]. The main problem is with the reproduction of the edges. From geometrical optics, we expect a sharp rise in intensity from 0 % (shaded area) to 100 % (the irradiated area). The real transition is shown in Fig. 2.9.

2.4 Preliminary Considerations for Lithography

Fig. 2.7

E-k diagram for nanocrystalline SiC

Fig. 2.8

(Optical) lithography

11

It turns out that the resolution of an image produced cannot be better than approximately one wavelength of the light used. In this context, “light” means anything that can be described by a wavelength. This includes x-rays, synchrotron radiation, electrons and ions. As an example, the wavelength of an incident electron is given by

O

h 2q V me

(2.1)

12

2 Quantum Mechanical Aspects

Fig. 2.9 Diffraction image of a black/transparent edge. l is a length which is equivalent to the wavelength of the incident light.

(h is the Planck constant, me the mass of electron, q the elementary charge, V the accelerating voltage). The different types of lithography, their pros and cons, and their future prospects will be discussed in the section about nanoprocessing.

2.5

Confinement Effects

In the early days of quantum mechanics, one considered the case of a particle, e.g., an electron that is confined in a tightly bounded potential well V with high walls. It is shown that within the walls (0 < x < a), the wave function of the electron is oscillatory (a standing wave) while it presents an exponential decaying function in the forbidden zone outside the walls (x < 0, x > a), Fig. 2.10. Thus, the particle’s behavior departs from the rule in two respects: (i) Discrete energy levels Ei and wave functions are obtained as a result of the demand for

Fig. 2.10

Particles in a potential well

2.5 Confinement Effects

13

continuity and continuous differentiation of the wave function on the walls [12]. This is contrary to classical macroscopic findings that the electron should be free to accept all energies between the bottom and the top margins of the potential well. (ii) The particle shows a non-vanishing probability that it moves outside the highly confined walls. In particular, it has the chance to penetrate a neighboring potential well with high walls. In such a case, we are dealing with the possibility of so-called tunneling. In anticipation, both consequences will be briefly shown with the help of examples. A detailed description will be given in the sections dedicated to nanodevices. 2.5.1

Discreteness of Energy Levels

The manufacturing of sufficiently closely packed potential wells in an effort to investigate the above-mentioned predictions has not been easy. Mostly they are investigated with the help of electrons which are bound to crystal defects, e.g., by color centers. Meanwhile, a good number of experimental systems via which quantization occurs are available. One example is the MOS varactor. Let us assume that it is built from a p-type wafer. We will examine the case in which it is operated in inversion. The resulting potential for electrons and the wave functions are schematically presented in Fig. 2.11. The normal operation of a MOS transistor is characterized by the electrons being driven from the source to the drain, i.e., perpendicular to plane of the figure. Ideally, they can only move within these quantum states (the real behavior is modified through phonon interaction). The continuation of this basic assumption leads to a way with which the fine-structure constant

Fig. 2.11

Potential and wave functions in a MOS structure operated in inversion

14

2 Quantum Mechanical Aspects

D

q2 2H 0 h c

(2.2)

can be measured with great accuracy, as developed in [13] (H0 is the dielectric constant of vacuum, c the velocity of light). 2.5.2

Tunneling Currents

Other systems manufactured are sandwich structures (e.g., GaAlAs–GaAs–GaAl As). They are based on the fact that GaAlAs for instance, has a band gap of 2.0 eV while GaAs has a band gap of only 1.4 eV. By applying a voltage, the band structure is bent as schematically presented in Fig. 2.12. In a conventional consideration, no current is allowed to flow between the contacts (x < 0, x > c) irrespective of an applied voltage because the barriers (0 < x < a and b < x < c) are to prevent this. However, by assuming considerably small values of magnitudes a, b, and c, a tunneling current can flow when the external voltage places the energy levels outside and inside (here E'') on the same value (in resonance). It should be noted that after exceeding this condition, the current sinks again (negative differential conductivity). This sandwich structure is the basis for a good number of devices such as lasers, resonant tunneling devices or single-electron transistors. They will be treated in the section on electrical nanodevices.

2.6

Evaluation and Future Prospects

The state of the available molecule and cluster simulation programs can be described as follows: the construction of a molecule occurs under strict ab initio rules, i.e., no free parameters will be given which must later be fitted to experiment; instead, the Schrödinger equation is derived and solved for the determination of eigenenergies and eigenfunctions in a strictly deterministic way. The maximum manageable molecular size has some 100 constituent atoms. The limitation is essentially set by the calculation time and memory capacity (in order to prevent difficulties, semi-empirical approximations are also used. This is done at the expense of the accuracy). Results of these calculations are x x x x

Molecular geometry (atomic distances, angles) in equilibrium, Electronic structure (energy levels, optical transitions), Binding energy, and Paramagnetism.

The deficits of this treatment are the prediction of numerous desired physical properties: temperature dependency of the above-named quantities, dielectric behavior, absorption, transmission and reflection in non-optical frequency ranges, electrical conductivity, thermal properties. However, there are attempts to acquire these properties with the help of molecular mechanics and dynamics [14–16].

2.6 Evaluation and Future Prospects

15

Fig. 2.12 Conduction band edge, wave function, and energy levels of a heterojunction by resonant tunneling

In numerous regards it is aim to bond foreign atoms to clusters. It is examined, for instance, whether clusters are able to bond a higher number of hydrogen atoms. The aim of this effort is energy storage. Another objective is the bonding of pharmaceutical materials to cluster carriers for medication depots in the human body. The above-named programs are also meant for this purpose. However, it should be stressed that great differences often occur between simulation and experiment, so that an examination of the calculations is always essential. Any calculation can only give hints about the direction in which the target development should run. As far as the so-called quantum-mechanical influences on devices and their processes are concerned, the reader is kindly referred to the chapters in which they are treated. However, we anticipate that the investigation for instance, of current mechanisms in nano-MOS structures alone has given cause for speculations over five different partly new current limiting mechanisms [17]. The reduction of electronic devices to nanodimensions is associated with problems which are not yet known.

4

Nanolayers

4.1

Production of Nanolayers

4.1.1

Physical Vapor Deposition (PVD)

In general, physical vapor deposition (PVD) from the gas phase is subdivided into four groups, namely (i) evaporation, (ii) sputtering, (iii) ion plating, and (iv) laser ablation. The first three methods occur at low pressures. A rough overview is seen in Fig. 4.1. (i) Evaporation. This procedure is carried out in a bell jar as depicted in Fig. 4.2. A crucible is heated up by a resistance or an electron gun until a sufficient

Fig. 4.1 Three fundamental PVD methods: evaporation (a), sputtering (b), and ion plating (c) [53]

40

4 Nanolayers

vapor pressure develops. As a result, material is deposited on the substrate. Technically, the resistance is wrapped around the crucible, or a metal wire is heated up by a current and vaporized. The electron gun (e-gun) produces an electron beam of, e.g., 10 keV. This beam is directed at the material intended for the deposition on the substrate. The gun’s advantage is its unlimited supply of evaporating material and applicability of non-conductive or high-melting materials. Its shortcomings lie in the production of radiation defects, for instance in the underlying oxide coating. Both procedures are more precisely depicted in Fig. 4.3. (ii) Sputtering. In literature, there is no clear definition of the term sputtering. Generally, an atom or a molecule, usually in its ionized form, hits a solid state (target) and knocks out surface atoms. This erosion is accompanied by a second process, namely the deposition of the knocked out atoms on a second solid state (substrate). The latter process is relevant when forming thin layers. (a) Glow discharge. In its simplest form, sputtering is achieved by glow discharge with dc voltage. A cross section of the arrangement is schematically represented in Fig. 4.4. After mounting the samples on a holder, the chamber is rinsed repeatedly with Ar. Eventually, a constant gas pressure of some 100 mPa is built up. The target, being attached a few centimeters above the substrate, is raised to a negative dc potential from 500 to 5 000 V, while both chamber and substrate are grounded. The discharge current requires a conducting target. When the voltage is slowly increased, a small current flows over the two electrodes. This current is caused by the ions and electrons which normally appear in the gas and by the electrons which leave the target after ion bombardment (secon-

Fig. 4.2 Vacuum system for the vaporization from resistance-heated sources. When replacing the transformer and heater with an electron gun, vaporization by means of an electron beam occurs [54].

4.1 Production of Nanolayers

41

(a)

(b)

Fig. 4.3 Evaporation by means of resistance-heating with a tungsten boat and winding (a) and electron gun (b) [55]

dary electrons). At a certain voltage value, these contributions rise drastically. The final current-voltage curve is shown in Fig. 4.5. The first plateau (at 600 V in our example) of the discharge current is referred to as Townsend discharge. Later the plasma passes through the “normal” and “abnormal” ranges. The latter is the operating state of sputtering. A self-contained gas discharge requires the production of sufficient secondary electrons by the impact of the ions on the target surface and conversely, the production of sufficient ions in the plasma by the secondary electrons. (b) High frequency discharge. When replacing the dc voltage source from Fig. 4.4 with a high frequency generator (radio frequency, RF, generator), target and substrates erode alternately depending on the respective polarity. But even with these low frequencies, a serious shortcoming becomes apparent: due to the substantially small target surface (compared to the backplate electrode consisting of the bell, the cable shield, etc.) a proportionally large ion current flows if this backplate electrode is negatively polarized. This would mean that the substrates are covered with the material of the bell, which is not intended.

42

4 Nanolayers

Fig. 4.4

DC voltage sputtering [56]

Fig. 4.5

Applied voltage vs. discharge current [56]

In order to overcome this shortcoming, a capacitor is connected in series between the high frequency generator and the target, and/or the conducting target is replaced with an insulating one. During the positive voltage phase of the RF signal, the electrons from the discharge space are attracted to the target. They impact on the target and charge it; current flow to the RF generator is prevented by the capacitor. During the negative half-wave of the RF signal, the electrons cannot leave the target due to the work function of the target material. Thus, the electron charge on the target remains constant. Due to their mass, the positively charged ions are not capable of following the RF signal with frequencies above 50 kHz. Therefore, the ions are only subjected

4.1 Production of Nanolayers

Fig. 4.6

(a) RF sputter system and (b) distribution of the potential in an RF plasma

Fig. 4.7

Ion plating system [57], slightly modified

43

to the average electrical field which is caused by the electron charge accumulated on the target. Depending on the RF power at the target, the captured charge leads to a bias of 1 000 V or more and causes an ion energy within the range of 1 keV. When using a capacitively coupled target, the limitations of the glow discharge can be overcome, i.e., a conducting target is no longer required. Therefore, the number of layers which can be deposited by sputtering is greatly increased. (iii) Ion plating. This process is classed between resistance evaporation and glow discharge. A negative voltage is applied to the substrate, while the anode is connected with the source of the metal vaporization. The chamber is subsequently filled with Ar with a pressure of a few Pa, and the plasma is ignited. After cleaning the wafer by sputtering, the e-gun is switched on and the material is vaporized. The growing of the layer on the substrate is improved by the plasma in some properties such as adhesion and homogeneity compared to a sole PVD. The advantages of ion plating are higher energies of the vaporized atoms and therefore better adhesion of the produced films. The disadvantage is heating of the

44

4 Nanolayers

substrate and plasma interactions with radiation-sensitive layers such as MOS oxides. (iv) Laser ablation. The following process data are typical values. A high-energy focused laser beam (100 mJ, 1 J / cm2) is capable of eroding the surface of a target rotating with a velocity of one revolution per second. The material is vaporized on the substrate, and as a result, a film is produced on it at a rate of 0.07 nm / laser pulse. The growth can be supported by heating the substrate (750 °C) and by chemical reactions (oxygen at 50 Pa). So far, the used lasers are excimer, Nd:YAG, ruby, and CO2 lasers. Advantages of laser ablation are the deposition of materials of high-melting points, a good control over impurities, the possibility of the vaporization in oxidizing environments, and stoichiometric vaporization. A shortcoming is the formation of droplets on the vaporized layer. A system described in the literature is presented in Fig. 4.8. 4.1.2

Chemical Vapor Deposition (CVD)

The CVD process is performed in an evacuated chamber. The wafer is put on a carrier and heated to a temperature between 350 and 800 qC. Four possible versions of the chamber are presented in Fig. 4.9. One or several species of gases are let in so that a gas pressure is formed between very low and normal pressure. The gas flow hits the wafer at a normal or a glancing incidence. Now a dissociation (in the case of a single gas species) or a reaction between two species takes place. In both cases, a newly formed molecule adheres to the wafer surface and participates in the formation of a new layer. Let

Fig. 4.8 Typical laser ablation system under O2 partial pressure [58]. Note the so-called plume, a luminous cloud close to the irradiated target surface. RHEED: reflection highenergy electron diffraction

4.1 Production of Nanolayers

Fig. 4.9

45

Four versions of a CVD chamber

us consider silane (SiH4) as an example of the first case. On impact, it disintegrates into elementary silicon, which partly adheres to the surface, and to hydrogen, which is removed by the pumps. The second case is represented by SiH4, which reacts with N2O to form SiO2. The process can of course be accompanied by other types of gases which act as impurities in the deposited layer. Examples are phosphine (PH3) or diborane (B2H6), which also disintegrate and deliver effective phosphorus or boron doping of the deposited silicon. In this book, the closer definition of CVD, i.e., a layer structure without the continuation of the underlying lattice, is used. The reverse case is called vapor phase epitaxy. In some publications, both expressions are used without any distinction. CVD deposition can be supported by an RF plasma, as schematically shown in Fig. 4.10, an example of an amorphous or micro-crystalline silicon deposition. The major difference to the conventional CVD is the addition of Ar for the ignition of the plasma and of H2. The degree of the SiH4 content in H2 determines whether amorphous or microcrystalline silicon is deposited. In the first step, both types are deposited. However, a high concentration of H2 etches the amorphous portion, and only the microcrystalline component remains. The etching process is even more favored if higher frequencies (e.g., 110 MHz) other than the usual 13.56 MHz are used. In Fig. 4.11, a typical PECVD system is depicted.

46

4 Nanolayers

Fig. 4.10

Block diagram of a PECVD system

4.1 Production of Nanolayers

4.1.3

47

Epitaxy

We are dealing with epitaxy if a layer is deposited on a (crystalline) substrate in such a way that the layer is also monocrystalline. The layer is often referred to as film. In many cases, the film takes 99.9 % of the entire solid state, as in the example of a Czochralski crystal, which is pulled from a narrow seed nucleus. If film and substrate are from the same material, we are dealing with homoepitaxy (e.g., silicon-on-silicon), otherwise with heteroepitaxy (e.g., silicon-on-sapphire). Another distinction is made by the phase from which the film is made: vapor phase epitaxy, liquid phase epitaxy (LPE), and solid state epitaxy. A subclass of vapor phase epitaxy is molecular beam epitaxy (MBE). The setup of a vapor phase epitaxy is not shown because it resembles the CVD setup shown previously to a good extent. However, the setup of a molecular beam epitaxy (MBE) is depicted in detail in Fig. 4.12.

Fig. 4.11

PECVD system for the deposition of amorphous solar cells

48

4 Nanolayers

The constituents of the deposited film are contained in mini furnaces as elements, the so-called Knudsen cells, which are discussed below. During heating some vapor pressure develops and an atom beam is emitted, which is bundled by successive apertures. The beam hits the wafer surface to which the atoms remain partially adhered. There, they can react with atoms of a second or third beam, which is also directed towards the wafer surface. A favorable reaction and finally the film deposition depend on the selection of the parameters, i.e., wafer temperature, the ratios of the beam densities, the purity of the surface, etc. As shown in the same figure, the effusion cell can be replaced by an evaporation with the electron gun. The chamber contains many devices for the in situ inspection of the growing layers, for example low energy electron diffraction (LEED), secondary ion mass spectroscopy (SIMS), and Auger and Raman spectroscopy. The quality of the vacuum is controlled by a residual gas analyzer. The effusion (Knudsen) cell is seen in detail in Fig. 4.13. The material to be deposited is contained in the innermost cell which is heated up. Its temperature is controlled by a set of thermocouples and resistance heaters. Without further measures, the high temperature leads to molecular desorption from all warmed up surfaces, to the emission of impurities into the substrate, and in the worst case, to the breakdown of the vacuum. Therefore, a screen cooled with liquid air is installed around the internal cell. Conversely, in order to avoid high thermal flows between furnace and screen, a water-cooled shield is inserted between them. For the operation of the LPE, knowledge of the phase diagram is required. Let us consider the phase diagram of Ga and As as an example (Fig. 4.14). This phase

Fig. 4.12

Schematic structure of the MBE as in [59]

4.1 Production of Nanolayers

Fig. 4.13

49

Effusion cell (schematic) from [60]

diagram represents the case of a congruent phase transition. The mixture of Ga and As in a ratio of 50:50 takes over the role of a constituent, i.e., the phase diagram disintegrates into a first Ga-GaAs and a second GaAs-As phase diagram. In other words: GaAs forms a stable compound which is not subjected to any chemical change during the change of temperature. Obviously, both diagrams are eutectic. Let us begin with a melt of GaxAs1x and a solid state of GaAs, both in close contact. In order to avoid sublimation of the As, the process should begin with a melt enriched with Ga so that we work on the left side of the phase diagram above the liquidus. Pure GaAs freezes out on the already available solid GaAs by decreasing the temperature (this is also the aim of LPE) and the melt becomes richer in Ga until finally only pure Ga remains. In the reverse case (operation on the right of GaAs), solid GaAs is again deposited but the melt is rich in As. Doping atoms can be added to the melt before the deposition, for instance, when fabricating p-n junctions. As an example, a GaAs wafer (the original solid state in the above example) is depicted in Fig. 4.15. The wafer is laterally pulled under different melts, so that the above mentioned deposition

50

4 Nanolayers

Fig. 4.14

Ga-As phase diagram [61]

Fig. 4.15

Sledge arrangement for the fabrication of injection lasers using LPE

process can be repeated with different material layers (Ga, GaAlAs) and different doping types. This process was the early way of fabricating an injection laser. Solid state epitaxy is a phenomenon which appears, for example, as a recrystallization of amorphous silicon. As is well known, ion implantation destroys the crystalline structure of silicon up to complete amorphization. If the wafer is annealed, the structure can be reorganized beginning from the unimpaired bulk of the wafer. This phenomenon is of less interest for nanotechnology. It should be mentioned that there are some versions of the classical epitaxial procedures as in-situ implantation or laser-enhanced deposition.

4.1 Production of Nanolayers

51

Finally, let us compare some typical parameters of the different types of epitaxy (Table 4.1). The best control of the thickness, highest purity, and largest doping gradients are obviously obtained by MBE. These advantages are compensated by high equipment costs and low growth rates.

Table 4.1

Comparison of epitaxial parameters [60]

Process characteristic Possibility of in situ etching

LPE

VPE

MBE

Yes, through melt back

Yes, through halide reaction with substrates above growth temperatures Possible by heat treatment in inert gas, but surface cannot be monitored except by ellipsometry

No

Further cleaning and monitoring of substrate surface

Not possible

Typical growth rate range Layer thickness control Substrate temperature (for growth of GaAs on GaAs) Interface control

0.1–1.0 µm / min

0.05–0.3 µm / min

r50 nm

r25 nm

1120 K

1020 K

Segregation and outdiffusion can occur

Autodoping and outdiffusion can occur

Topography

Very difficult to obtain uniformly smooth surfaces over large areas

Can be very smooth but conditions for success are somewhat critical

Composition Composition control of ternaries determined by and quaternaries process chemistry

Composition determined by process chemistry

Total carrier concentration in undoped film

Low, (ND + NA) | 1014 cm3

Very low, (ND + NA) | 1013 cm3

Yes, by ion bombardment or thermally in UHV. Can be monitored by AES, LEED or RHEED, but there may be electron beam effects 0.001–0.03 µm / min Easily r5 nm, can be r0.5 nm 820 K

Only outdiffusion, but this may occur at enhanced rates under some conditions Extremely smooth surfaces obtained under not very critical conditions. Even initial surface roughness is smoothened out. Group III element ratio determined by thermal stability of the source. Group IV ratio by surface chemistry Rather high, (ND + NA) t 1016 cm3

52

4 Nanolayers

Table 4.1 (cont’d) Process characteristic Presence of deep levels

Range of dopants available

Control of dopant incorporation

Process amenable to automation

4.1.4

Comparison of epitaxial parameters [60] LPE

VPE

MBE

Yes, NT | 1012–1014 cm-3, low end of range fairly easily realizable A wide range, most groups II, IV and VI elements can be used. Limited only by solubility in liquid metal and should have a low vapor pressure over the solution at the growth temperature Range available 1014–1019 cm-3, but only flat profiles can be produced, i.e., sudden changes in doping level cannot be obtained Probably not, too operator dependent

Yes, NT | 1012–1014 cm-3, low end of range fairly easily realizable A very wide range of II, IV and VI elements. Limited only by need for solubility of element or a decomposable compound

Yes, NT | 1012–1014 cm-3, but low end of range difficult to achieve A rather narrow choice, Si, Sn (ntype) Be, Mn (Mg) p-type

Range available 5·1014–1019 cm-3 and reasonably sharp changes in dopant concentration (spatial resolution |30 nm)

Range available 5·1016 – 1019 cm-3. With sharp changes in dopant concentration (spatial resolution |5 nm)

To some extent, but some process steps would still be operator dependent

The whole process can be automated.

Ion Implantation

The Accelerator Ion implantation is a doping technique with which ions are shot into a substrate (e.g., a silicon wafer) using an accelerator. The basic principle is presented in Fig. 4.16. The desired ion species is let in as a gaseous compound through a needle valve (alternatively, solid state sputtering sources are used). The compound is dissociated and ionized with an electron beam. The arising ions (including the unwanted ones) are pulled out of the source area and brought to an energy of 30 keV by a first, preliminary acceleration (all figures are typical values). Then, the ions pass through a magnetic field filter which is adjusted in such a way that only the desired ion type can run into the acceleration tube. The magnetic field filter is based on the fact that the Lorentz force for a moving charged particle compels a circular path. The radius of the circle depends on the magnetic field B, the velocity v, and the mass m of the particle. More exactly, it depends on m / e (e is the elementary

4.1 Production of Nanolayers

53

charge). For the desired ion species, i.e., for a given m / e, the magnetic field is adjusted in such a way that the circular path of these particles terminates exactly at the end of the accelerator tube. There, the ions acquire a total energy of 360 keV. This energy can be doubled or multiplied by the use of double or multiple charged ions. However, the ion yield, i.e., the available ion current, is exponentially reduced with the state of charge (ionization state).

Fig. 4.16

Ion implantation equipment (schematic) [62]

54

4 Nanolayers

The beam can be positioned by a combination of an aperture with a Faraday cage. With two capacitor disks each, the beam can be scanned upwards and downwards or left and right. In order to avoid Lissajou figures, horizontally and vertically incommensurable scanning frequencies are chosen. The beam current is measured by an ammeter, which is connected to the substrate holder isolated against ground. The substrate holder is designed as a carousel, for example, in order to be able to implant several samples without an intermediate ventilation. Calculation of the Implantation Time Typical required dose values NI lie between 1012 and 1016 cm2. The necessary implantation time depends on the available beam current, I, on the irradiated substrate surface, A, and on the charge state of the ions. The ions summed in the irradiation time t represent a charge Q = q NI A, whose relation to the ion beam results in the irradiation time: t

Q I

q NI A . I

(4.1)

As an example, an ion current of 1 µA, a substrate surface of 100 cm2, and a dose of 1013 cm2 deliver an irradiation time of 160 s. This result applies to the charge state 1 (simple ionization) of the ions. For double, triple, etc. charged ions, the implantation time must be doubled (tripled, etc.). It should be noted that for multiple charged ions an equivalent multiple current is measured. Lattice Incorporation, Radiation Damage, Annealing The penetrating ions pass through the lattice depending on the ion mass/lattice atom mass ratio and the momentary velocity in a zigzag path (Fig. 4.17) At the jags of the path, the ions impinge on host lattice atoms, which leave their places and go to the interstitial site. Thus, lattice defects of different nature develop.

Fig. 4.17

Path of an implanted ion in a lattice

4.1 Production of Nanolayers

55

The simplest defect—the Frenkel defect—is produced by the displacement of a lattice atom into an interstitial site. Thus, a vacancy and an interstitial atom develop. Vacancies can possess different charge states (e.g., neutral, positive, negative, double negative). Furthermore, they can form aggregates with foreign atoms and influence their diffusion. Double vacancies can be formed if an impinging ion dislodges two nearest neighbor lattice atoms. Moreover, they can be formed by two single vacancies. Double vacancies are stable up to approximately 500 K. Dislocations can develop by the association of single defects, or they grow from unannealed radiation damage into undamaged area during annealing. Dislocation lines anneal only at high temperatures (t1000 °C), and very often they do not anneal at all in implanted layers. Further defects can be formed by the accumulation of vacancies and interstitial atoms as well as by the association of foreign atoms with vacancies or interstitial atoms. If many lattice atoms are displaced by an impact ion in a considerably small volume, a locally amorphized area develops. Often, this area is known as cluster, and its exact structure is unknown. In ion implantation, one always expects this case because of the high mass and energy of the impact particles. Accordingly, the possible processes during implantation and subsequent temperature annealing are complex and hardly accessible to theoretical description. The implanted ion comes to rest usually on an interstitial site after numerous impacts. Thus, contrary to intention, it cannot work as a dopant (Recall: the 15th electron of phosphorus can only be detached with small energy expenditure by embedding the atom into the lattice structure and emerge as a free electron in the crystal). Annealing is applied for both the annealing of lattice defects and for the relocation of the doping atoms from interstitial sites into lattice sites, i.e., a thermal treatment of the implanted samples at approximately 900–1100 °C in a suitable atmosphere like nitrogen or hydrogen gas. The ratio of electrically active ions sitting on lattice sites to the total number of implanted ions is called activation. Usually, the activation rises monotonously with temperature. In the case of phosphorus, for example, almost complete activation is achieved at approximately 700 °C. However, there are exceptions like in the case of boron where an intermediate minimum can occur (Fig. 4.18). The intermediate minimum of the boron implantation is caused by the behavior of the interstitial silicon atoms, which are produced by the nuclear impacts during the implantation. At approximately 500 °C, they try to return to lattice sites thereby pushing the already existing boron atoms in lattice sites back to interstitial sites. Implantation Profile To a first approximation, the distribution of the implants is described by a Gaussian curve: N ( x)

N max e

§ x R p ¨ ¨ 'R 2 p ©

· ¸ ¸ ¹

2

.

(4.2)

56

4 Nanolayers

Fig. 4.18 (a) Electrically active phosphorus atoms in Si. Dose values are 1.1·1013, 1.1·1014, and 6·1014 cm2, implantation energies 20 and 40 keV, (b) electrically active phosphorus atoms in Si. Dose values are 1·1013, 1·1014, and 1·1015 cm2, implantation energies 20, 30, and 50 keV. According to [63], slightly modified

Rp is the position of the center of the distribution (for the Gaussian curve, this is identical to the maximum position), 'Rp the full width at half maximum of the distribution (Fig. 4.19). N(x) has the of dimension of cm3. The concentration, Nmax, in the maximum of the distribution is calculated from the implanted doses NI, [NI] = cm2: f

³ N ( x) dx

NI

0

or

Fig. 4.19

Simplified distribution of the implants in the substrate

(4.3)

4.1 Production of Nanolayers

N max # 0.4 N I / 'R p .

57

(4.4)

As a prerequisite for the validity of Eq. 4.2, the implantation profile must not diffuse by annealing. A second prerequisite is the prevention of an implantation into a low indexed crystal orientation. Thus, the crystal must act amorphous for the ion beam. If one shoots toward a low indexed crystal orientation, then the ion beam runs without resistance through the lattice channels and reaches substantially large depths (channeling), Fig. 4.20. Channeling is avoided by tilting the crystal, which is aligned in (100) direction against the ion beam, usually by 7° as depicted in Fig. 4.21. The Gaussian function used in Eq. 4.2 is only an approximation of the distribution predicted by theory. This “exact” distribution cannot be expressed by an analytic function. Rather, the ion profile can be subjected to the so-called “moment development”. This procedure can be roughly compared to a series expansion of a function for Fourier coefficients or a multipole development: the ion profile N(x) is multiplied by 1, x, x2, etc. and integrated over the entire semiconductor depth x. The function f(x) can be reconstructed from the developing numerical values (the moments). These numerical values arise from transport-theoretical considerations. At least the first four moments can be illustrated: ³ N(x) dx describes the zero moment identical to the implanted dose, ³ x N(x) dx describes the first (static) moment of the center of the distribution, ³ x2 N(x) dx delivers its straggling and ³ x3 N(x) dx its skewness (asymmetry). Just from these descriptions alone, the Gaussian function is obviously attractive for describing the profiles: from the above integrations, this function delivers Rp as a center, 'Rp as full width at half maximum, and zero as skewness. In all technically important cases, it is sufficient to describe skewed profiles by joining two Gaussian functions with the half widths V1 on the right and V2 on the left of the maximum. Let Rm denote the position of the maximum; Rp is only equal

(a)

(b) Fig. 4.20

(a) Si crystal in (110) direction and (b) misaligned by 7°

58

4 Nanolayers

Fig. 4.21 Dependency of the depth distribution of 32P after 40 keV (a) and 100 keV (b) implantation. The angles indicate the deviations from the (110) direction [64].

to Rm when V1 = V2. Thus, N ( x)

N ( x)

2 (V 1  V 2 ) 2ʌ 2 (V 1  V 2 ) 2ʌ

( x  Rm ) 2

e

2V 12

for x t Rm , and

(4.5)

( x  Rm ) 2

e

2V 22

for x d Rm .

In reference tables, however, the energy Rp, 'Rp, and the standardized third moment CM3p / ('Rp)3 are listed (Table 4.2). The way of getting back from this data to V1, V2, and Rm is complicated. The equation CM 3 p

V

3 p

ª § ǻ ǻ « 2 0.8  0.256¨ ¨V p Vp « © ¬

· ¸ ¸ ¹

2

º » » ¼

(4.6)

with known CM3p / (Vp)3 and Vp is solved for ' / Vp and subsequently ' = (V1 

4.1 Production of Nanolayers

59

V2) / 2 is obtained. With this background, the second equation 2

§ ǻ · §V · ¸ 1 ¨ m ¸  0.44¨ ¨V p ¸ ¨V p ¸ ¹ © ¹ ©

2

(4.7)

is solved for Vm = (V1 + V2) / 2, and thus V1 and V2 are given. Finally, Rm is given by: Rm

R p  0.8(V 2  V 1 ) .

(4.8)

If the third moment is negative, V1 and V2 must interchange their roles. 4.1.5

Formation of Silicon Oxide

Thin oxide layers are contained in almost all electronic devices. They appear as gate oxide in MOS transistors or MIS solar cells, field oxide for isolation purposes, antireflection layers in solar cells, or as passivation layers for long-term protection. We begin with thermal oxidation. A Si wafer is cleaned so that any organic or heavy metal impurity on the surface is removed and the natural oxide is dissolved. Then, the wafer is inserted in a quartz tube heated to a temperature of about 1100 °C. A flow of an oxidizing gas, either pure oxygen (dry oxidation) or nitrogen driven through water (wet oxidation), is maintained. When oxygen penetrates into the substrate, the Si surface reacts with the oxygen and forms silicon dioxide. While this procedure sounds simple, it requires highest cleanliness, which is the critical step for the MOS production. Figures 4.22 and 4.23 show graphs of the oxide thickness vs. oxidation time for several temperatures [66]. Numerous scientific and technical investigations have focused on the properties of silicon dioxide. Fields of interest are the growth laws, deep levels, capture of charge carriers from the silicon, segregation and rearrangement of the dopant in the neighboring silicon, masking properties against diffusion and ion implantation, etc. Their in-depth discussion is beyond the scope of this book. Technical alternatives to thermal oxidation are CVD and PECVD of oxides. These are treated in the section on CVD. There are some technical CVD versions such as TEOS deposition shown in Fig. 4.24. A feed gas (usually nitrogen) is driven through a container filled with tetraethylorthosilicate (TEOS). TEOS is a liquid at room temperature. Its chemical structure is presented in Fig. 4.25. The enriched nitrogen flows to the wafers where SiO2 is deposited on their surfaces. The deposition is maintained at a temperature of about 650 to 850 °C by means of an external induction coil. It should be noted that the silicon in the TEOS is already oxidized, in contrast to the silane process. In this state, TEOS finds only limited application because the deposition temperature (>650 °C) prevents its use after metallization. In order to obtain lower deposition temperatures, the application of a more aggressive oxidant, i.e., ozone, is required. After adding some few molar per cent of ozone, the optimum deposition temperature is reduced to 400 °C.

60

4 Nanolayers

Table 4.2 Ranges, standard deviation, and third moment (beside other parameters) for boron implantation with energies of 10 keV to 1 MeV [65] LSS range statistics for boron in silicon. Substrate parameters Si: Z = 14, M = 28.090, N = 0.4994·1023, U / r = 0.3190·102, H / e = 0.1130, CNSE = 0.3242·102, P = 2.554, J = 0.8089, SNO = 0.9211·102 Ion B: Z = 5, M = 11.000 Northcliffe constant = 0.292·104 Energy, keV 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 550 600 650 700 750 800 850 900 950 1000

Projected range, µm 0.0333 0.0662 0.0987 0.1302 0.1608 0.1903 0.2188 0.2465 0.2733 0.2994 0.3248 0.3496 0.3737 0.3974 0.4205 0.4432 0.4654 0.4872 0.5086 0.5297 0.5708 0.6108 0.6496 0.6875 0.7245 0.7607 0.7962 0.8309 0.8651 0.8987 0.9317 0.9642 0.9963 1.0280 1.0592 1.1356 1.2100 1.2826 1.3537 1.4233 1.4917 1.5591 1.6254 1.6909 1.7556

Projected standard deviation, µm 0.0171 0.0283 0.0371 0.0443 0.0504 0.0556 0.0601 0.0641 0.0677 0.0710 0.0739 0.0766 0.0790 0.0813 0.0834 0.0854 0.0872 0.0890 0.0906 0.0921 0.0950 0.0975 0.0999 0.1020 0.1040 0.1059 0.1076 0.1092 0.1107 0.1121 0.1134 0.1147 0.1159 0.1171 0.1182 0.1207 0.1230 0.1252 0.1271 0.1289 0.1306 0.1322 0.1337 0.1351 0.1364

Third moment ratio estimate -0.031 -0.309 -0.483 -0.617 -0.727 -0.821 -0.904 -0.978 -1.046 -1.108 -1.166 -1.220 -1.271 -1.319 -1.364 -1.408 -1.449 -1.489 -1.527 -1.564 -1.634 -1.699 -1.761 -1.820 -1.876 -1.930 -1.981 -2.030 -2.078 -2.125 -2.170 -2.214 -2.257 -2.298 -2.339 -2.435 -2.526 -2.614 -2.697 -2.778 -2.856 -2.933 -3.006 -3.079 -3.149

Lateral standard deviation, µm 0.0236 0.0409 0.0555 0.0682 0.0793 0.0891 0.0980 0.1061 0.1135 0.1203 0.1266 0.1325 0.1380 0.1431 0.1480 0.1525 0.1569 0.1610 0.1649 0.1687 0.1757 0.1821 0.1880 0.1936 0.1988 0.2036 0.2082 0.2125 0.2166 0.2205 0.2242 0.2277 0.2311 0.2344 0.2375 0.2448 0.2515 0.2576 0.2633 0.2687 0.2737 0.2784 0.2829 0.2871 0.2912

4.1 Production of Nanolayers

61

Table 4.2 (cont’d) Ranges, standard deviation, and third moment (beside other parameters) for boron implantation with energies of 10 keV to 1 MeV [65] Energy, keV Range, µm 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 550 600 650 700 750 800 850 900 950 1000

0.0623 0.1100 0.1536 0.1940 0.2317 0.2673 0.3010 0.3331 0.3638 0.3934 0.4218 0.4494 0.4761 0.5020 0.5272 0.5518 0.5759 0.5993 0.6223 0.6448 0.6886 0.7309 0.7718 0.8116 0.8503 0.8880 0.9249 0.9610 0.9964 1.0311 1.0651 1.0987 1.1317 1.1642 1.1962 1.2745 1.3506 1.4246 1.4969 1.5678 1.6373 1.7056 1.7728 1.8391 1.9046

Standard deviation, µm 0.0141 0.0221 0.0276 0.0316 0.0347 0.0371 0.0392 0.0409 0.0424 0.0437 0.0449 0.0459 0.0468 0.0476 0.0484 0.0491 0.0497 0.0503 0.0509 0.0514 0.0523 0.0532 0.0539 0.0546 0.0552 0.0558 0.0564 0.0569 0.0573 0.0578 0.0582 0.0586 0.0589 0.0593 0.0596 0.0604 0.0611 0.0618 0.0624 0.0629 0.0634 0.0639 0.0644 0.0648 0.0653

Nuclear energy loss, keV / µm 96.86 75.89 63.09 54.43 48.12 43.28 39.44 36.30 33.68 31.45 29.52 27.85 26.37 25.05 23.88 22.81 21.85 20.97 20.17 19.43 18.11 16.97 15.98 15.10 14.32 13.62 12.99 12.42 11.90 11.42 10.98 10.58 10.20 9.854 9.530 8.809 8.192 7.659 7.193 6.781 6.415 6.088 5.792 5.525 5.282

Electronic energy loss, keV / µm 102.2 144.0 175.8 202.3 225.4 246.1 264.9 282.2 298.4 313.4 327.7 341.1 353.9 366.0 377.6 388.7 399.4 409.7 419.5 429.1 447.1 464.0 479.9 494.9 509.1 522.6 535.4 547.5 559.1 570.2 580.7 590.9 600.6 609.9 618.8 639.6 658.6 675.8 691.7 706.2 719.5 731.8 743.2 753.6 763.3

The anodic oxidation [67] is shown in Fig. 4.26. The wafer is immersed into a 0.04 M solution of KNO3 in ethylene glycol with a small addition of water. After mounting it to a holder with a vacuum, it is positively charged, while a platinum disk acts as a backplate electrode.

62

4 Nanolayers

Fig. 4.22

Oxide thickness vs. oxidation time (wet oxidation)

The current causes a reaction on the surface of the silicon: Si  2H 2 O  4h  o SiO 2  4H 

(4.9)

CH 2 OH  CH 2 OH o 2HCHO  2H   2e 

(4.10)

H 2 O o 12 O 2  2H   2e 

(4.11)

Technically, anodic oxidation is of little importance. The quality of the oxide is too low, and the process is time-consuming or not compatible with other applications. Rarely, sol gels are used to manufacture oxide layers. During this process, a suspension of oxide particles in an organic solvent is distributed over the wafer. A centrifuge facilitates homogeneous distribution of the liquid on the wafer. Then, the wafer is baked and the solvent evaporates. The required temperatures range from 500 to 800 °C. The oxide can have the quality of a gate oxide, but no largescale application has been reported so far. A further manufacturing process is SOI (silicon-on-oxide), i.e., the implantation of oxygen up to the stoichiometric dose and its reaction with silicon to form SiO2 (see Sect. 4.1.4 on ion implantation). SOI has gained in importance because of better radiation resistance and heat distribution compared to conventional technologies.

4.2 Characterization of Nanolayers

Fig. 4.23

Oxide thickness vs. oxidation time (dry oxidation)

Fig. 4.24

TEOS process

4.2

Characterization of Nanolayers

4.2.1

Thickness, Surface Roughness

63

In the following chapter, some methods to determine nanometer-thin layers are presented. They are demonstrated with the help of measurement setups.

64

4 Nanolayers

Fig. 4.25

Structure of tetraethylorthosilicate (TEOS)

Fig. 4.26

Assembly of the anodic oxidation of silicon (schematic)

Admittance Bridges A metal oxide semiconductor (MOS) diode is produced by the oxidation of a Si wafer with, for instance, an oxide of 10 nm thickness and metal evaporation on the oxide (this structure being the middle part of the so-called MOS transistor). From the specifications of the evaporation (or the lithography), area A of the metal point is known. The measurement of the oxide thickness is performed with the help of an admittance (or capacitance) bridge (Fig. 4.27). Additionally, the substrate is operated in accumulation by applying a bias voltage (attraction of majority carriers to the silicon boundary surface). The modulating frequency of the bridge

4.2 Characterization of Nanolayers

65

should be as low as possible in order to suppress the resistance of the silicon bulk. A good choice is 200 Hz. A detailed description is given in the section on the determination of the doping level and profile (Sect. 4.2.4.) The measured capacitance is caused by the oxide alone. Therefore, it is called Cox. Now the equation for the parallel-plate capacitor can be applied to give the oxide thickness: d ox

H ox

A Cox

(4.12)

where A is the area of the metal point, and Hox = 3.4·1013 F / cm. Michelson Interferometer Measurements It is presupposed that the film can be etched locally in such a way that (i) a sharp edge develops, and (ii) the exact thickness of the film to be measured is removed at the etched position. This case is frequently implemented, for instance, if SiO2 is etched by HF with high selectivity against Si (i.e., the etching stops when the Si is reached). Another case is a thin layer of lightly-doped silicon on a carrier of heavily doped silicon. The surface, which has a step, is made reflective by metal evaporation and inserted into a Michelson interferometer as shown in Fig. 4.28. Two parallel sets of bright and dark interference fringes appear to the viewer. They are shifted against each other by 'N. The height of the step and thus the thickness of the film d is given by: d

Fig. 4.27

'N

O 2

.

Measurement of the oxide layer with an admittance bridge

(4.13)

66

4 Nanolayers

Fig. 4.28 Michelson interferometer [68]. L is the light source, M1 and M2 are mirrors, C is a disk for the compensation of the double way A–D–A by the beam splitter S. M2' is the virtual image of M2. O1 and O2 are the objective lenses.

Tolanski Method This method is referred to as a special case of a multiple-beam interference. The method can be explained in two steps: (i) Multiple beam interference (Fig. 4.29). After passing through a glass plate, each beam is partially reflected (R) and partially transmitted (T) because of a thin silver film. According to Airy’s formula, the intensities can be described by: IT

I max 1  F sin 2 (k G / 2)

(4.14)

with the phase difference kG

2ʌ

O

2n1 t cos T

2ʌN ,

(4.15)

the finesse (i.e., the separation of adjacent fringes per width of half max) F

and

4R , (1  R) 2

(4.16)

4.2 Characterization of Nanolayers

Fig. 4.29

I max

67

Multiple-beam interference (modified from [68] and [69])

T2 . (T  A) 2

(4.17)

n1: the refractive index of the medium between the mirror glasses. A: absorption of the mirrors DF and LJ T: transmission of the mirror R: reflection of the mirror. With a sufficient reflection, R (# 95 %), transmitted light becomes narrow bright fringes on a dark background if irradiation is done with monochromatic light. In reflection, narrow dark fringes on a bright background are seen. There, the prerequisite of constructive interference is fulfilled: N

1, 2, 3...

(4.18)

(ii) Fizeau strips. The sample preparation resembles that of the above-described Michelson experiment. The sample to be measured is prepared in such a way that a part of the film is etched or the substrate is already partly exposed during deposition (Fig. 4.30a). Now it used instead of the lower glass plate of Fig. 4.29, and the upper glass plate is tilted against the sample at a small angle. When illuminating with a monochromatic (point) source, an interference pattern is obtained for interferences of the same thickness. More precisely, two interference fringes shifted against each other develop again. Their misalignment, 'N (which can also be a fractional number), yields the film thickness: d

'N

O 2

.

(4.19)

If the interference patterns of the etched side lie exactly between the strips of the unetched side, 'N ½ and the film thickness d O / 4 . A result is depicted in Fig. 4.31.

68

4 Nanolayers

Fig. 4.30

Sample preparation for the Tolanski method: (a) Fizeau plate, (b) sample

Fig. 4.31

Tolanski measurement (schematic)

Fig. 4.32 Interference patterns of the emitted infrared radiation by 0.55 µm polycrystalline silicon deposition on Si3N4 [70, slightly changed]. Reactant: SiH2Cl2–H2. Deposition temperature: 1120 °C. Detector: PbS—2.0 µm filter. Evidence: infrared radiation

In Situ Method An example of the measurement of the layer thickness during the deposition of polycrystalline silicon on silicon nitride is given in Fig. 4.32. By flowing SiCl4/H2 or SiH2Cl2/H2 gas over a Si3N4 substrate, polycrystalline silicon is deposited on the substrate by the dissociation of the silane. Due to the high temperature of 1120 °C, the sample emits infrared light, and selected fre-

4.2 Characterization of Nanolayers

69

quencies can be observed (here 2.0 µm). Because of multiple interference in the film, an interference pattern develops. With otherwise constant parameters (wavelength, observation direction), the interference changes continuously between constructive and destructive interference with progressive growth. The same interference patterns are obtained if an external monochromatic source is used. Frequency Shift of a Quartz Crystal Oscillator During the deposition of metallic films, a quartz resonator is placed in the proximity of the material that is to be deposited. This quartz reduces its resonance frequency with the thickness of the film deposited on it. The frequency change is converted into units of the layer thickness. This procedure is not very exact. Errors are caused by the different distances of resonator/deposition source and substrate/deposition source. Moreover, the unknown initial treatment of the quartz leads to an irreproducible behavior. A separate correction factor must therefore be determined for each metal. Ellipsometry As a rule, the thickness of either one or two transparent films on an opaque substrate is measured with the ellipsometer. An elliptically polarized monochromatic beam impinges on the surface of the film (Fig. 4.33). The incident wave is characterized by the amplitudes of the parallel (see below) and the perpendicular (see below) components and the phase difference ' between these two components. After reflection at both surfaces and the summation of all beams, the relation between the amplitudes and the phase difference is modified. This modification depends on x x x x

the refractive indices n2, n3 of film and substrate, the absorption coefficients k2, k3 of film and substrate, the incidence angle M1, and the film thickness d.

On condition that the optical constants n3 and k3 are known and that the film is transparent, i.e., k2 = 0, the refractive index and the thickness of the film are determined from a quite simple experiment (Fig. 4.34). Monochromatic light is first linearly polarized by a polarizer, and then elliptically polarized by a retarder (quarter wave retarder). After reflection at the film, the light passes through a further polarizer for analysis and is subsequently observed with a telescope. For didactic purposes, let us exchange the sequence of the compensator and the film. Additionally, let us define a reference plane, for instance, the plane of incidence, E. It contains the incident and outcoming beams and the perpendicular. The terms parallel and perpendicular refer to this plane, furthermore to the numerical angles of the quarter wave retarder, the polarizer, and the analyzer. The polarizer (in an arbitrary position) produces a linearly polarized oscillation, which may be

70

4 Nanolayers

Fig. 4.33

Geometric and material definitions in the ellipsometer experiment

Fig. 4.34

Ellipsometer [71]

split up into a parallel and a perpendicular fraction. The two fractions have a phase difference ' = 0. After reflection the new phase difference ' of the two fractions transforms a linear oscillation into an elliptical oscillation of the form: x 2 y 2 2 x y cos ǻ   AB A2 B 2

sin 2 ǻ .

(4.20)

A and B are the amplitudes of the two oscillation directions in the previous coordinate system (Fig. 4.35). It should be noted that the phase angle ' between the components of the ellipse applies to the selected coordinate system only. By rotating the coordinate system, the phase changes. In particular, ' = S / 2 holds if the large semiaxis and the new x' axis coincide. Such a coordinate transformation takes place if the elliptically polarized beam is exposed to a quarter wave retarder. Its two polarization directions are put in the directions of the ellipse axis so that the fast beam corresponds to the lagging component of the ellipse (angle of rotation - of the quarter wave retarder from the x-direction). Since the two beams

4.2 Characterization of Nanolayers

Fig. 4.35

71

Oscillation ellipse after reflection

catch up with each other again, a linearly polarized beam develops, which can be brought to extinction with an analyzer. The direction of the linearly polarized beam to the reference plane is K. K (rather: K + S / 2) is measured with the analyzer, - is known as the direction of rotation of the quarter wave retarder. The criterion of the correct determination of K and - is the extinction of the beam behind the analyzer. Thus, the axes ratio of the ellipse is given as tan J

tan(K  - ) .

(4.21)

The knowledge of this angle enables us to determine the ratio of the oscillation components B / A = tan \ in the reference plane system: cos 2\

cos 2 J cos 2- .

(4.22)

For the phase difference ' in the reference plane system, we find tan ǻ

tan 2 J . tan 2G

(4.23)

What has been achieved so far? Originally, a linearly polarized beam with the components A0 (parallel to the reference or incidence plane) and B0 (perpendicular to it) is produced in the polarizer. This beam has the phase difference '0 = 0 (otherwise it would not be linearly polarized) and the amplitude ratio \0 = B0 / A0, which is known from the rotation of the polarizer against the reference plane by the angle \0. A particularly simple solution is obtained in the case of a 45° rotation; A0 = B0, or tan \0 = 1. This method enables us to determine how the amplitude ratio and the phase difference have changed due to reflection. If a theoretical statement can be made on the \-' change resulting from the reflection at a thin film of a thickness d and refractive index n2 [i.e., tan \ / tan \0 = f(d, n2) and ('  '0 = f(d, n2)], then the determination of the layer thickness and refractive index should be possible by forming the inverse functions d(\, ') and n2(\, ').

72

4 Nanolayers

The theory of Fresnel and Neumann offers a solution. Its knowledge, however, is not required for the operation of the ellipsometer, as will be shown below. For historical reasons, the procedure is done somewhat differently without changing the basic idea. First, the compensator is usually set behind the reflecting surface. Therefore, the sequence is polarizer–sample–compensator–analyzer. Second, one does not rotate the compensator but the polarizer (for the compensator, a direction of r45° of the fast axis is maintained against the reference plane). Thus, by varying the amplitude ratio B0 / A0, the ellipse created after reflection is rotated. If the position of the compensator is adjusted correctly, the elliptical oscillation is brought back into a linear form. If the angles \ and 'are determined in this way, then these two values can be brought into a set of curves where ' is presented as a function of \. The parameters are film thickness (in units of wavelength or as phase difference 2Sn2 d / O) along a '-\ curve and the refractive index which has a fixed value for each '-\ curve. An example of such a curve set is found Fig. 4.36. These curves are calculated according to the Fresnel Neumann theory. For each wavelength, angle of inclination of the two polarization levers against the sample and path difference of the compensator, a new record of curves must be calculated. In our graph, many specializations have taken place. For instance, the quarter wave retarders can be replaced by a compensator of any path difference. The analysis must then be corrected accordingly. Moreover, we have not treated the other pairs of solutions for the compensator and analyzer angle. Furthermore, an accurate discussion about the determination of the direction of rotation of the ellipse must be done. This is connected with the question about the sign of the directions of rotation during the measurement and the trigonometric functions. At last, we neglected the question of how the absorption influences the measurement. It should be noted that the ellipsometer can easily be automated by a microprocessor controller. Of course, a technique is required that enables us to deter-

Fig. 4.36 '-\ curve set. Parameters are phase angle 2Sn2 d / O (along a curve) and n2 (from curve to curve); normal angle of the ellipsometer levers M1 = 70°, n3 = 4.05 (silicon), extinction coefficient of the silicon k3 = 0.028, O = 546.1 nm [71]

4.2 Characterization of Nanolayers

73

mine the two angles of rotation of analyzer and polarizer simultaneously. Such devices are commercially available. A completely different approach consists of measuring the ellipse by rotating the analyzer photometrically (with the multiplier). Such devices have been constructed as well. In the above discussion, a homogeneous layer is assumed whose refractive index is constant with depth. Two values ' and\ are measured, which deliver the thickness and the refractive index. However, our assumption can be invalid if, for instance, one or more films are deposited on the first one, or if the conditions of the depositions are changed so that a refractive index profile is produced. Therefore, an improved model and a sophisticated instrumentation is required. Instead of using a single ellipsometer wavelength, the whole available spectrum can be used. This method is known as spectroscopic ellipsometry, which requires new approaches in data evaluation. On the basis of well known technological data such as film thickness, film material, and profiles, a model of the layer structure can be set up and the spectral '-\ curves can be determined. The model is subsequently improved by fitting the resulting '-\ curves to the measured curves. The knowledge on some layers is so good that the derived profile even delivers physical models of the film. As an example, the ratio of amorphous to microcrystalline fractions can be determined during growth of amorphous films. The surface roughness of the substrate can be determined, and the transition layers between substrate and film or between the films can be resolved to within Ångströms. In spectroscopic ellipsometry, the components of the dielectric function H rather than ' and \ are plotted. The transformation of ' and \ to H is given by

H1

§ tan 2 M1 (cos 2 2\  sin 2 2\ sin 2 ǻ) · ¸¸ and sin 2 M1 ¨¨1  (1  sin 2\ cos ǻ) 2 ¹ ©

(4.24a)

H2

sin 2 M1 tan 2 M1 sin 4\ sin ǻ . (1  sin 2\ cos ǻ) 2

(4.24b)

An example of the dielectric function (H2) depending on the crystalline state of Si is shown in Fig. 4.37. An evaluation of the dielectric function and the transformation to a layer model is depicted in Fig. 4.38. Profilometer A thin film, whose thickness is to be measured, is grown on a substrate. Therefore, the sample is partly covered with wax or photoresist so that a sharp edge between the covered and untreated surface is given. The untreated surface is etched in acid, which removes the film but does not attack the substrate (selective etching). Consequently, the edge deepens in the sample. Now, the cover (wax) is removed. The edge’s depth is measured with a needle, which is moved across the edge and which is sensitive to changes in the surface. (Fig. 4.39). The vertical position of the needle is checked with a piezoconverter (with step heights larger than 2 nm) or an inductive converter (with step heights larger than

74

4 Nanolayers

Fig. 4.37 Dielectric functions for amorphous, polycrystalline, and monocrystalline Si [72]

Fig. 4.38

Layer sequence derived from spectroscopic ellipsometry [72]

some micrometers). These machines are called Talysurf or Talystep. An example of a measurement is shown in Fig. 4.40. When small edge differences are to be measured, the major difficulty in the handling of the device is the leveling of the unetched surface serving as measuring reference. If this plane and the needle’s path do not correspond, the noise during the high measurement amplification will prevent a reasonable determination of the height. In the meantime, however, selfadjusting versions are available. Scanning Tunneling Microscopy (STM), Atomic Force Microscopy (AFM) x

STM. The surface of a conducting material is covered with an electron cloud, whose density reduces with increasing distance from the surface.

4.2 Characterization of Nanolayers

Fig. 4.39

75

Thickness measurement with a needle

Fig. 4.40 Measuring an edge with an inductive needle [73]. Quartz deposition on glass substrate. Test ridges are produced by removing the mask. Vertical magnification 1,000,000 fold, one small division represents 2 nm. Horizontal magnification 200fold, one small division represents 0.025 mm. Thickness of the deposited layer (mean value) approximately 26 nm (25.9 mm on the diagram)

x

If a metal tip is within a close distance to this surface, a current flows between the tip and the surface. The current flow begins from a distance of about 1 nm, and it decreases by a factor of 10 for every reduction of 0.1 nm in the distance. This phenomenon can be used for an x-y presentation of the roughness. When moving the tip laterally, a constant current is maintained by following the distance of the tip. The necessary adjustment is a measure of the roughness. The fitting is done with piezoelectric actors. These piezoelements can displace the tip with a minimum increment of 107 mm / V. AFM. Basically, this system consists of a cantilever with a tip, a deviation sensor, a piezoactor, and a feedback control (Fig. 4.41). If the tip is within a small distance to the surface, an atomic force develops between the tip and the surface so that the cantilever is bent upwards. A regulator keeps a constant force to the surface of the sample. The input signal for the regulator is laser light, which is reflected by the cantilever and which is sensitive to its position.

76

4 Nanolayers

Fig. 4.41

Atomic force microscope (schematic) [74]

Two images of the surfaces of CVD diamond films after thermochemical polishing (Fig. 4.42) are shown as examples of such a measurement. With AFM it is possible to determine a surface roughness in the nanometer range.

4.2.2

Crystallinity

The crystalline state of a material is best investigated with a diffraction experiment (Fig. 4.43). A monochromatic& x-ray or electron beam impinging on a crystal with & & the three primitive axes a , b , and c is assumed. An electron beam of energy E can be considered as a wave with the wavelength

O [Å]

12 E [eV]

.

(4.25)

& The wave vector of the incoming wave is k with k = 2S / O. The wave vector k ' of the scattered wave has the same wavelength O. The phase difference between the incoming beam serving as a reference and the outgoing beam is && && & 'I (k a  k ' a ) 'k a . (4.26)

Now, all scattered amplitudes from every lattice point must be added together. The & vector a is generalized to a vector & & & & U manb oc . (4.27) The total amplitude is proportional to & & & & & & & A e  i U 'k e i ( m a n b o c ) 'k

¦

¦

&

U

¦e m

m , n ,o & &  i m a 'k

¦e n

& &  i n b 'k

¦e o

& &  i o c 'k

.

(4.28)

4.2 Characterization of Nanolayers

50 µm

77

40 nm

25 0 nm

0

(a)

25

50 µm

(b)

Fig. 4.42 (a) SEM images of an as-grown CVD diamond film of optical grade—average surface roughness of 30 µm (profilometer measurement), (b) AFM image of the same surface after thermochemical polishing—average surface roughness of 1.3 nm [75]

The intensity, I, of the scattered beam is proportional to |A2|. Every sum of the right hand side of Eq. 4.28 can be written in the form M 1

¦e m 0

& &  i m ( a 'k )

&

&

1  e  i M ( a 'k ) &

&

1  e i ( a 'k )

.

(4.29)

In order to get the total intensity, we multiply Eq. 4.29 (and the other two sums) by their conjugate complexes. This delivers

Fig. 4.43

Scattering of a plane wave through a crystal consisting of M 3 atoms

78

4 Nanolayers

I1

& & sin 2 [ M (a 'k ) / 2] . & & sin 2 [(a 'k ) / 2]

(4.30)

The graph of Eq. 4.30 is a curve with sharp maxima (“lines”). The maxima occur for & & a 'k 2 ʌq (4.31a) where q is an integer. This is one of Laue’s equations. The other two are & & b 'k 2ʌr and & & c 'k 2ʌs .

(4.31b) (4.31c)

The curve sketching of Eq. 4.31a shows, for instance, that the maximum height for I1 is v M 2, while the width is v 2S / M. I1 is proportional to its height (v M 2) times its width (v 1 / M), i.e., proportional to M. Thus, the intensity of the central reflex, I, is proportional to M 3 in three & dimensions. & & We define a new set of vectors A , B , C , which satisfy the relations && & & & & A a 2ʌ B a 0 Ca 0 & & & & & & B b 2ʌ (4.32) Ab 0 Cb 0 && && && Bc 0 Ac 0 C c 2ʌ . If these vectors are additionally normalized in the form & & & b uc A 2ʌ & & & a b uc & & & c ua B 2ʌ & & & a b uc & & & a ub C 2ʌ & & & , a b uc then every vector & & & & 'k q A  r B  s C

(4.33)

(4.34)

with & &integer & numbers q, r, and s is a solution of the Laue equations. The vectors A , B , C define the fundamental vectors of the reciprocal lattice. It should be noted that only the contribution of the lattice structure to the diffraction pattern has been regarded up to now. Of course, the so-called atomic scattering factors must be considered for the calculation of the expected intensities, i.e., the scattering ability per atom. If two sources of irradiation are compared regarding the investigation of thin films, it turns out that a thin film of a few na-

4.2 Characterization of Nanolayers

79

nometers diffracts an electron beam so that useful information can be obtained while the same film is not suitable for x-ray diffraction. X-ray diffraction (XRD). There are several ways to utilize the Laue equations. One of them is white light irradiation, i.e., a broad x-ray spectrum is illuminated on the crystal to be examined. The crystal (or& rather all sets of lattice planes) interacts with the light of the wavelength (i.e., 'k ) that fulfills the Laue equations. This method offers some advantages such as a quick determination of the crystal symmetry and orientation. As a disadvantage, the lattice constant cannot be determined. Vice versa, a monochromatic beam can be used, which is exposed on the powder of a crystal to be examined. Therefore, there is always a great number of crystallites (powder grains) in the correct orientation for a given wavelength so that the Laue equations are fulfilled again. The important information is the intensity as a function of the diffraction angle. For crystalline materials, the wafer is usually rotated (e.g., by an angle T). Simultaneously, the detector is rotated by an angle 2T (Bragg-Brentano diffractometer). An efficient version of XRD is x-ray topography. The fundamental idea consists of aligning the crystal which to be examined in such a way that a reflection is measured under a certain angle. A perfect crystal should maintain the diffraction intensity if the beam (or rather the crystal) is shifted laterally. Every imperfection of the crystal violates the diffraction equations. Usually, the structure is created in such a way that a first reference crystal is carefully adjusted so that a sharp monochromatic beam is produced. This one is in turn directed toward the crystal, which should be measured, shifted perpendicularly to the beam. An example is given in Fig. 4.44. Additionally, the system can be improved by “rocking” the crystal perpendicularly to the plane of incidence (Fig. 4.45). As an advantage of this rocking setup, extremely small deviations in the lattice constant can be picked up. If, for instance, heteroepitaxial films are deposited, two (a doublet line) instead of only one signals are sometimes found. This means that the film still differs from the substrate.

(a)

(b)

Fig. 4.44 (a) Wafer before heat treatment and (b) after formation of dislocations by oxidation at 1200 °C. Examined with x-ray topography [76]

80

4 Nanolayers

Electron diffraction is performed in vacuum with a monoenergy beam and stationary samples. In a first version known as low energy electron diffraction (LEED), voltages between 10 V and 1 kV are used. The diffracted electrons are observed in reflection with a fluorescent screen (Fig. 4.46). In order to avoid wrong signals due to surface impurities, the vacuum must be maintained under 109 Pa. LEED is used in order to measure the so-called surface reconstruction, i.e., the termination of a

Fig. 4.45

X-ray topography with a rocking setup [77]

Fig. 4.46

Electron diffraction at low energy (schematic) [78]

4.2 Characterization of Nanolayers

81

surface by a new type of lattice (“superlattice”). A typical LEED pattern is shown in Fig. 4.47.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Fig. 4.47 LEED patterns showing the effect of oxygen on the epitaxy of copper on a tungsten (110) surface. (a) Clean tungsten, (b) half a mono layer of oxygen on the tungsten, (c) two mono layers of copper—note the appearance of poorly oriented diffraction spots in the outer copper layer, (d) ten layers of copper, (e) heating to 300 °C for 5 min (resulting in some improvement of the orientation and in the reappearance of the tungsten beams), (f) heating to 550 °C for 15 min, (g) heating to 850 °C for 1 min (tungsten oxide as evidenced by the diagonal rows of beams about the tungsten beam position, (h) heating to 1050 °C for 1 min and returning to half a monolayer of oxygen on the tungsten [79]

82

4 Nanolayers

Another well-known version is the reflection high-energy electron diffraction (RHEED) as depicted in Fig. 4.48. Applied energies range from 10 to 100 keV. In order to avoid the penetration of these high-energy electrons into the lower-lying substrates, the operation is done under narrow glancing angles. RHEED is often used for in-situ monitoring of the growth of an epitaxial film (see the section on epitaxy). An example of an RHEED measurement is shown in Fig. 4.49. 4.2.3

Chemical Composition

Secondary ion mass spectroscopy (SIMS) is usually done to detect impurities and their profiles in solid states (Fig. 4.50, [82]).

Fig. 4.48

Reflection high-energy electron diffraction (schematic) [80]

(a)

(b)

Fig. 4.49 RHEED pattern: (00.1) Cu2S overgrowth on (111) Cu. (a) [ 1 1 0 ] Cu azimuth showing a weak [12.0] pattern of (00.1) Cu2S, (b) [ 2 1 1 ] Cu azimuth showing a weak [10.0] pattern of (00.1) Cu2S [81]

4.2 Characterization of Nanolayers

83

Primary ions (PI) from the ion source (IS) are accelerated to the sample (SP) in order to knock atoms off the surface. This process is called sputtering or ion milling. Some of the sputtered ions are electrically accelerated; they can be pulled out to a mass spectrometer (MS) where they are analyzed. Essentially, SIMS can be operated in two ways: (i) The composition of the wafer (more precisely, that of the surface zone) is determined by the analysis of the secondary ions. This is done with the mass spectrometer (Fig. 4.51). (ii) If the spectrometer is set to depths at a fixed mass, the measured intensity vs. sputtering time is a measure of the impurity density vs. depth. Calibrated samples are used for the transformation of the ion signal (current from a signal processor) into an ion density. Similarly, the removal rate must be known for the transformation of the sputtering time into a depth. The great advantage of the method is the possibility to measure all elements (even those in interstitial positions) and the high detection sensitivity of between 1015 and 1018 cm3, depending on the element. To obtain a constant atomization rate, it is necessary to use a stable ion gun. The atomization can be achieved either by a finely focused beam, which can be scanned on the surface to be analyzed, or by a beam with a constant current density distribution throughout the radius. In the first case, one has additionally the possibility to record an “ion image” by synchronizing the deflecting plates with an oscilloscope. The ionization rate strongly depends on the gas coverage on the sample. In particular, oxygen can increase the ionization rate up to a factor of 100. Therefore, sputtering is done with oxygen in some systems. If not, there is always a starting effect always, i.e., an apparently higher foreign atom concentration on the surface due to the unavoidable oxygen allocation.

Fig. 4.50 Schematic representation of a SIMS system: PI: primary ions, IS: ion source, BL: beam forming lens, MF: mass filter, DP: deflection plate, FL: focusing lens, SP: sample, SI: secondary ions, TO: transfer optics, EF: energy filter, MS: mass spectrometer, ID: secondary ion detector, VP: vacuum pumps

84

4 Nanolayers

Cr+

CrO+ Al

+

Cu+ Ga+ B+

+

P

As+

Fig. 4.51 Mass spectrum of a Cr layer of 50 nm thickness on Cu substrate, detected by SIMS [83]

20

20

10

15 min 1000 °C / H2

60 min 1000 °C / H2 Concentration, cm-3

Concentration, cm-3

10

19

10

10

[H] 18

10

[O]

0.0

0.5

1.0

1.5

2.0

2.5

[H]

18

10

17

10

19

3.0

[O] 17

10

0.0

0.5

1.0

Depth, µm

20

120 min 1000 °C / H2

Concentration, cm-3

Concentration, cm-3

2.5

3.0

20

19

240 min 1000 °C / H2 19

10

10

[H] 18

[O]

10

[H] [O]

18

10

17

17

0.5

1.0

1.5

2.0

Depth, µm

Fig. 4.52

2.0

10

10

100.0

1.5

Depth, µm

2.5

3.0

10

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Depth, µm

Hydrogen and oxygen profiles after hydrogen implantation in Cz silicon [84]

Noble gases are used as primary ions. The selection of the primary energy is a compromise. On the one hand, it must be large enough for a sufficient sputtering yield. On the other hand, a too high energy simply causes ion implantation and a small sputtering yield. Typical SIMS energies range from 5 to 10 keV. The prob-

4.2 Characterization of Nanolayers

85

lems of the procedure are the adjustment of constant sputtering rates, of plane surfaces, and of signals unimpaired by noise. Two examples of the possibilities of SIMS are shown below. In the first example (Fig. 4.52), an oxygen-rich Cz wafer is implanted with hydrogen and annealed in hydrogen for 15 to 240 min. The depth profiles of water and oxygen, recorded simultaneously, reveals hydrogen to work as a getter center for oxygen. After 120 min the original hydrogen is almost evenly distributed, while the oxygen maintains its sharp profile. The second example (Fig. 4.53) proves the feasibility of nanolayers by ion implantation. Conventional boron implantation with an energy of 500 eV and plasma-assisted diborane implantation with an energy of 350 eV are done. Activation occurs with rapid thermal annealing in order to prevent the widening of the original Gaussian curve or outdiffusion. A similar profiling procedure is based on the Auger electron emission. Again, sputtering is applied in order to drive through the depth of the layer. However, the signal is now gained by a process that is schematically shown in Fig. 4.54. An incoming x-ray quantum or a high-energy electron removes an electron from the inner shell (step 1). The deficiency is compensated by an electron from an outer shell (step 2), as shown in the center section of the figure. In a third step, a part of the free energy is transferred to another electron of the outermost shell that gains the remainder as kinetic energy (alternatively, an x-ray quantum can be emitted, right part of Fig. 4.54). The energy in step 2 is the difference of discrete energies, the ionization energy in step 3 is a discrete energy. Therefore, the remaining kinetic energy is likewise a discrete energy. All discrete energies are specific for the respective atoms in whose shell the processes happen. Thus, the kinetic energy identifies the material under investigation like a fingerprint (the same applies to the emitted x-ray quanta). A typical Auger electron spectrum is depicted in Fig. 4.55. Since the Auger lines are put on a rather broad background, they are detected more easily by differentiating the energy distribution N(E). Therefore, the ordinate of the usual Auger spectrum is converted to the function dN / dE. Electronic dif-

Fig. 4.53

SIMS depth profiles of boron [85]

86

4 Nanolayers

Fig. 4.54

Auger emission process [86]

ferentiation can easily be done with velocity analyzers superimposing a small alternating voltage to the energy-selecting dc voltage and with synchronously recording the output of the electron multiplier. The line height of the Auger signal is usually proportional to the surface concentration of the element causing the Auger electrons. Contrary to SIMS, Auger electron spectroscopy (AES) can verify the binding state of the material under investigation. The reason is the weak influence of the binding configuration and the neighboring atomic positions on the shell energies. This effect is called chemical shift. Auger measurements can be performed during a sputtering process. The Auger signal of a selected element is measured as a function of the depth. The procedure is similar to SIMS measurement (additionally, the exciting electrons or x-rays can be replaced by sputtering ions. This is called AES ion excitation). An example of such a deep measurement is Ta deposited on polycrystalline Si (Fig. 4.56). When using such a combination, one is interested in the cleanliness of the deposition (i.e., the incorporation of impurity atoms) and in the subsequent chemical reactions between the materials. 4.2.4

Doping Properties

Doping Type The Seebeck effect, also known as thermoelectric effect, can be used to determine the doping type. Two metal contacts, for example needle tips, are mounted on the

4.2 Characterization of Nanolayers

Fig. 4.55

Auger spectrum of InAs [87]

Fig. 4.56

Ta, Si, and O profiles of a TaSi2 film on Si by means of AES [88]

87

semiconductor. One of the two needles is heated up. With an n-type doping, a positive voltage (and a negative voltage with a p-type doping) is measured at the hot needle relative to the cold needle.

88

4 Nanolayers

Doping Level, Conductivity, Mobility In this section, the terms carrier density and doping level are used without distinction since silicon, the most important material to us, is in saturation at room temperature, i.e., each doping atom contributes one free charge carrier. Ideally, the semiconductor represents a cuboid with the edge lengths a, b, and c (Fig. 4.57). Two opposite surfaces are brought in contact by evaporation or coating with a conductive paste. The metal must ensure an ohmic contact. No electric rectifying effects or other current-voltage non-linearities may occur. The applied voltage, V, and the subsequent current, I, are measured. The two measured values are converted into the current density j, j = I / (a c), and the electric field E, E = V / b. From j = V E, the conductivity, V, results. The doping level, ND or NA, is obtained from an experimentally acquired reference table (ND or NA vs. V). A direct measurement of the doping level will be shown below. But technically, a semiconductor is mostly available as a round disk or a rectangular chip with a thickness of some 100 µm. In this case, the four-probe measurement can be conveniently used (Fig. 4.58). Four parallel needles at a distance of 0.635 mm from each other are mounted on the semiconductor. A current, I, is fed through the outer needles resulting in a voltage drop in the semiconductor. The

Fig. 4.57

Determination of the conductivity

Fig. 4.58 Four-probe measurement (not to scale). If the current feed is also put on the inner needles, a two-probe measurement is performed.

4.2 Characterization of Nanolayers

89

voltage between the inner needles, V, is measured with a high-ohmic voltmeter. The quotient V / I is a direct measure of the specific resistance of the semiconductor, U. The correction factor between V / I and U must be determined by the potential theory or by comparative measurements. The current and voltage distributions and thus the correction factor depend closely on the distance of the measuring needles and the radius of the disk. For a disk with an infinite radius, the correction factor is 4.53, so that the surface resistance R = 4.53V / I, and the resistivity U = R d (with a disk thickness d). As an advantage of this procedure, neither the contacts nor any resistances falsify the measurement. In some cases (e.g., when measuring an inhomogeneous doping process), one has to give up the advantages of the four-probe measurement, and the two-probe measurement is applied. Here, the feed current and the applied voltage are measured in only one pair of points. A correction factor between V / I and U is also needed. The pros and cons of the two-point measurement are described in the section on the measurement of impurity concentration profiles. As stated earlier, the doping values can also be determined from the specific conductivity. In a simplified physical consideration, each doping atom contributes exactly one electron to the increase of the electron density, n, which leads to an increase of the conductivity because

V

qPn

(4.35)

(q is the electron charge, µ the mobility). The question of which conductivity is obtained with a certain doping (or which measured conductivity corresponds to which doping) can be best answered from experience. The conductivities of several samples of different dopings have been measured, and the curves of U vs. ND and U vs. NA have subsequently been plotted. (for historical reasons, the specific resistance U is plotted instead of the conductivity). ND and NA are the doping densities for electron and hole doping. These curves are called Irvin curves. A representation is depicted in Fig. 4.59 [89]. It should be clear that a current-voltage measurement delivers only the product of the charge carrier density n (or p) and the mobility of the electrons (or holes) when considering Eq. 4.35. To separate the product, a second equation (second measurement) is necessary: the Hall experiment. Basically, let us assume the parallelepiped sample shown in Fig. 4.57. However, a magnetic induction B is applied to the sample in a direction perpendicular to the current flow (Fig. 4.60). As a result of the Lorentz force FL

qv B,

(4.36)

the charge carriers are deflected from their straight-line course between the electrodes. The direction of the Lorentz force is perpendicular to the current and original path (giben by v) and also perpendicular to the field direction (B). The charge carriers are collected on a cuboid surface, whose normal is perpendicular to I (or v) and to B. At the same time, a backward force Fe

q EH

(4.37)

90

4 Nanolayers

Fig. 4.59

Specific resistance as a function of the doping

Fig. 4.60

Experimental setup of the Hall effect (schematic)

develops due to an electric field caused by the accumulation of the electrons on the cuboid’s surface (this field must not be mistaken with the field causing the current I). In the stationary case, the forces are equal so that q v B = q EH, or after multiplying by the electron density n: (q n v) B

q n EH .

(4.38)

The product q n v represents the current density. The term RH determined from the measurements is known as the Hall constant: RH

EH jB

1 . qn

(4.39)

The electron density n (the hole density p for a hole semiconductor) is obtained from this term. From the sign of the Hall constant, the information whether electrons or holes are present is obtained. This procedure can be extended to a simultaneous measurement of the resistivity U and the Hall mobility µH. The four contacts A, B, C, and D are mounted on

4.2 Characterization of Nanolayers

Fig. 4.61

91

Measurement setup according to van der Pauw [90]

the edge of a thin sample that can have an arbitrary form (Fig. 4.61). The resistance RAB,CD is defined as the quotient of the potential drop VD  VC and the feed current between the contacts A and B causing the voltage drop. The resistance RBC, DA is defined analogously. The resistivity

U

· §R ʌ d R AB, CD  RBC , DA f ˜ ¨ AB , CD ¸ . ¨ RBC , DA ¸ ln2 2 ¹ ©

(4.40)

The factor f is obtained from the implicit equation ª (R /R )  1 ln 2 º cos « AB ,CD BC ,DA » ¬« ( R AB ,CD / RBC ,DA )  1 f ¼»

1 2

e

ln 2 f

.

(4.41)

The Hall mobility is determined by measuring the change in the resistance RBD,AC by an applied magnetic field:

PH

d 'R AC , BD . B U

(4.42)

The method described above is named after van der Pauw [90]. Another way of determining the doping level is the use of an MOS diode. A typical cross section of such a device has already been shown in Fig. 4.27. A bias is applied between the two metal contacts, and an alternating voltage modulation (usually 25 mV) is superimposed on it. In our case, an alternating voltage frequency of 1 MHz is used. The modulation is employed in order to measure the small signal capacitance. This is repeated for all bias values, for instance, between +10 to 10 V, so that a capacitance-voltage curve can be plotted (Fig. 4.62). The minimum/maximum capacitance ratio Cmin / Cmax (also marked with Cinv / Cox) is determined by the oxide thickness and, more importantly, by the doping level. With known oxide thickness, this relation can be calculated and pre-

92

4 Nanolayers

Fig. 4.62

High frequency C-V curve in equilibrium (n-type semiconductor)

Fig. 4.63

Nomograph for the determination of doping from the ratio Cmin / Cmax [91]

sented in the form of a nomograph with the oxide thickness as an additional parameter (Fig. 4.63). The determination of the oxide thickness dox is discussed in Sect. 4.2.1. Doping Profile In some cases, a doping results, whose value changes with the depth into the semiconductor, i.e., a profile (for instance, after diffusion, implantation or oxidation). Important measuring methods are:

4.2 Characterization of Nanolayers

93

(i) Beveling and two-probe measurement. In the first step, a probe tip is mounted on the surface of a semiconductor; the lower surface of the semiconductor is grounded (Fig. 4.64). The theory shows that the applied potential of the needle drops about to zero in the semiconductor within a length of approximately three spherical radii of the needle tip. Thus, the resistance between needle and back side is determined only by the resistance within three spherical radii or the doping in this volume. But often there is a high impedance layer, a p-n junction, or an oxide within the semiconductor or on its backside. In this case, the hemispherical potential distribution is violated. Thus, a second needle is usually mounted on the semiconductor surface as counter electrode in a second step. Here, almost half of the applied potential drops symmetrically within three radii (please note the relation to the four-point measurement: the two-points can be compared to the outer needles of the four-point measurement. Thus, the two additional points of the four-point measurement brought in between detect only a small fraction of the potential applied on the outer points). When performing a profile measurement, that means: the sample, which has been implanted, diffused, etc., is cut into chips and beveled in a third step (Fig. 4.65). The beveling angle depends on the depth profile; typical values are between 0.5° and 10°. The two points are placed on the beveled surface parallel to the beveled edge, and the local resistance is measured. Afterwards, the two needles are moved over the beveled surface and the measurement is repeated. The measurement path along the beveled surface is converted into the depth in the semiconductor (this requires the exact knowledge of the beveling angle). The counting begins from the edge of the beveled surface. In this way, the local resistance is determined as a function of the depth of the semiconductor. The resistance can again be transformed into the doping density using calibration curves. A coverage of the surface with an oxide (as in the case of an MOS structure) is helpful for the determination of the beveled edge since in this case, a clear jump in the resistance occurs. An example of such a measurement (a buried boron layer in n-type silicon) is presented in Fig. 4.65. (ii) MOS profile measurement. The MOS capacitance is the result of a series circuit of the oxide capacitance Cox and the space charge capacitance of the semiconductor Csc (Fig. 4.66).

Fig. 4.64

One and two probe measurements

94

4 Nanolayers

Fig. 4.65 Bevel of an n-type sample implanted with 56 MeV boron and the related resistivity profile. The boron has been activated in nitrogen atmosphere for 30 minutes at 800 °C [92].

Fig. 4.66

High frequency MOS equivalent circuit (simplified) and voltage definitions

4.2 Characterization of Nanolayers

95

In the following, let us only consider the transition zone of the C-V curve, which is rising strictly monotonously (Fig. 4.61), or more precisely, only the section under the so-called flat band point. From these capacitances measured in high frequency Chf,, the oxide capacitance is subtracted by applying the series circuit. Thus, the space charge capacitance remains. The latter delivers the position where the doping is measured (where HSi = 1.04 1012 F / cm): A H Si . C sc

x

(4.43)

On the contrary, the space charge capacitance can be calculated from Poisson’s equation. Let M be the partial voltage (from the total applied voltage) that drops over the space charge zone in the silicon. The integration of Poisson’s equation (first with a constant doping) d 2M dx 2



qN

(4.44)

H Si

together with Eq. 4.43 delivers:

M



q N H Si 1 . 2 2 C sc

(4.45)

If N is dependent on x and hence on M, Eq. 4.45 must be written in differential form. The solution for N yields N ( x)

r

3 C sc 1 . d C q H Si sc dM

(4.46)

The sign results from the sign of the doping charge. The calculation of the partial voltage M from the applied voltage V is not trivial. The usual way consists of calculating Csc vs. M with the doping as a parameter and subsequently Chf vs. V. A slight adjustment for high frequency has to be done, and the free charge carriers must be considered. From the adjustment of the measured values, M vs. V is obtained. Another procedure circumvents this calculation and the adjustment, but it requires the additional measurement of the low frequency capacity Clf vs. V. Thus, N ( x)

r

2 1 C /C 2Cox lf ox q H Si 1  Chf / Cox

§ d (Cox / Chf ) · ¨ ¸ ¨ ¸ dV © ¹

1

(4.47)

and 1

x

· § Chf ¸ . ¨ ¨ H Si (1  Chf / Cox ) ¸ ¹ ©

(4.48)

96

4 Nanolayers

(iii) Rutherford backscattering (RBS). This procedure is shown in Fig. 4.67. First, let us assume an undoped crystal that is exposed to a helium beam (sometimes also a hydrogen beam). The beam is produced by an accelerator. All particles have the same energy E0 (usually 1 MeV). The sample is aligned in such a way that the particles arrive toward a so-called low-indexed channel axis. In this case, the crystal appears to the particle as consisting of channel tubes and thus, to a large extent, it appears hollow (for a better understanding, please consider a crystal model). Thus, 95 % of the incoming beam can penetrate into the channels, while only 5 % hit the walls of the channels. A small fraction of it is scattered in the direction of a particle detector that is set up to the surface in a direction different from that of the beam. The detector is energy-dispersive. Thus, it can distinguish the backscattered He particles according to their energy. Since all detected particles are scattered under the same angle and with identical conditions (masses, energies), they have lost the same energy during impact on the surface. Ideally, they all should have the same kinetic energy in the backscattering spectrum. If the near-surface of the crystal is doped, He atoms that already penetrated the channels of the crystal can be scattered again toward the detector on impact with the doping atoms. In particular, this applies to doping atoms that are inserted in interstitial sites, but large—in relation to host lattice atoms—doping atoms inserted in lattice sites also scatter the He beam quite well. On its way in the crystal, the He atom has given off energy. The deeper the scattering position, the smaller the energy that is registered in the detector. From this remaining kinetic energy, the position of the scattering atom can be calculated by the loss of energy per distance. The more doping atoms at this position, the higher the number of particles assigned to this kinetic energy. Thus, the backscattering spectrum is a representation of the profile. It must only be read backwards. Thus, a small energy means a deep position of the doping atoms (Fig. 4.68).

Fig. 4.67

Rutherford backscattering (schematic)

4.2 Characterization of Nanolayers

97

Fig. 4.68 Backscattering spectra: (a) Irradiation of the crystal in a random direction (no channeling), (b) irradiation of an implanted crystal in a channel direction, (c) irradiation of a non-implanted crystal in a channel direction. The energy E0 E1 is the recoil energy of a Si surface atom.

The results of an RBS measurement of an Au-Ni-Au layer sequence on a silicon substrate (Fig. 4.69) are shown in Fig. 4.70. It should be considered how well the Ni layer of 15 nm thickness is detected. As a result of the impact laws, it is apparent that RBS is particularly sensitive to heavy ions. 4.2.5

Optical Properties

Interference colors of thin layers. A first estimate of the thickness of a thin transparent layer deposited on an opaque substrate is obtained based on its color. Therefore, color charts have been developed for the most important cases, SiO2 and Si3N4 [94–96] (Tables 4.3. and 4.4).

Fig. 4.69 Used layer sequence for an RBS measurement [93]. The lower Au layer of 40.5 nm might rather be labeled with Au-Ge, cf. Fig. 4.70.

98

4 Nanolayers

Fig. 4.70 RBS spectrum for the layer sequence of Fig. 4.69 [93]. The broad curve between the channels 360 and 410 reflects the uppermost Au layer (153.8 nm), the Gaussianlike curve around channel 350 the intermediate Ni layer (16.5 nm). The layer underneath consists of a homogeneous Au/Ge alloy (40.5 nm), it appears as a double peak (channel 290 and 300) since Au and Ge have different recoil energies. The primary energy of the He2+ probe beam is 2 MeV.

Table 4.3

Colors of SiO2

Film thickness, Color µm 0.05 Tan 0.07 Brown

0.10

Dark violet to red violet

0.12 0.15

Royal blue Light blue to metallic blue

0.17

Metallic to very light yellow-green Light gold or yellowslightly metallic Gold with slight yelloworange Orange to melon colored (dark pink)

0.20 0.22 0.25

Film thickness, Color µm 0.63 Violet-red 0.68 “Bluish” (not blue, but border line between violet and blue green. It appears more like a mixture between violet-red and blue-green and over-all looks grayish. 0.72 Blue-green to green (quite broad) 0.77 “Yellowish” 0.80 Orange (rather broad for orange) 0.82 Salmon 0.85

Dull light-red-violet

0.86

Violet

0.87

Blue-violet

4.2 Characterization of Nanolayers Table 4.3 (cont’d) Film thickness, µm 0.27 0.30 0.31 0.32 0.34 0.35 0.36 0.37 0.39 0.41 0.42 0.44 0.46 0.47 0.48 0.49 0.50 0.52 0.54 0.56 0.57

0.58 0.60

Table 4.4

Colors of SiO2

Color

Film thickness, µm Red-violet 0.89 Blue to violet-blue 0.92 Blue 0.95 Blue to blue-green 0.97 Light green 0.99 Green to yellow-green 1.00 Yellow-green 1.02 Green-yellow 1.05 Yellow 1.06 Light orange 1.07 Carnation pink 1.10 Violet-red 1.11 Red-violet 1.12 Violet 1.18 Blue-violet 1.19 Blue 1.21 Blue-green 1.24 Green (broad) 1.25 Yellow-green 1.28 Green-yellow 1.32 Yellow to “yellowish” (not 1.40 yellow but is in a position where yellow is to be expected. At times it appears to be light creamy grey or metallic) Light-orange or yellow to 1.45 pink borderline Carnation pink 1.46

Color Blue Blue-green Dull yellow-green Yellow to “yellowish” Orange Carnation pink Violet-red Red-violet Violet Blue-violet Green Yellow-green Green Violet Red-violet Violet-red Carnation pink to Salmon Orange “Yellowish” Sky blue to green-blue Orange

Violet Blue-violet

Colors of Si3N4

Film thickness, µm 0.01 0.077 0.025 0.034 0.035 0.043 0.0525 0.06 0.069

Color Very light brown Average brown Brown Brown-pink Pink-lila Intensive lila Intensive dark-blue Dark-blue Average blue

Film thickness, µm 0.095 0.105 0.115 0.125 0.135 0.145 0.155 0.165 0.175

Color Light blue Very light blue Light blue-brownish Light brown-yellow Very light yellow Light yellow Light to middle yellow Average yellow Intensive yellow

99

100

4 Nanolayers

Reflection, absorption, transmission, and refractive index are measured with optical standard devices (e.g., Xe high-pressure lamps, laser, monochromators, spectroscopic ellipsometers). Other systems are developed for Raman, cathodoluminescence, photoluminescence, and electroluminescence measurements. An example of the result of an absorption measurement is given in Fig. 4.71. The steep fall around 1.1 µm reflects the Si gap of 1.12 eV. Fourier transform infrared spectroscopy (FTIR). FTIR belongs to the paragraph about transmission/reflection measurements. However, it has become so important that it merits special discussion. For this purpose, let us return to the Michelson interferometer of Fig. 4.28. A mirror M1, which is moved forwards and backwards (variation of L1) parallel to its perpendicular, is assumed. The mirror M2 is positioned at a fixed distance L2. The thickness of the balance disk and the beam splitter is neglected. The sample is held between the beam splitter and detector. For simplification a monochromatic light source of the wavelength O and the frequency f = c / Ois assumed. Constructive interference results if L1 equals L2 (the distance between beam splitters and mirror M1). If L1 and L2, however, differ about a quarter of a wavelength (O / 4), the path difference is O / 2, and destructive interference occurs. During the movement of the mirror M1, an interference pattern of the intensity I(x) is observed behind the sample: I ( x)

2ʌ x f · § B( f ) ¨1  cos ¸. c ¹ ©

(4.49)

B ( f ) is the product of the light source and the transmission of the sample. The monochromatic light is now replaced with light having a spectral distribution. Then the intensity is modified to

Fig. 4.71

Absorption coefficient of Si at 300 °C vs. wavelength [97]

4.2 Characterization of Nanolayers

§

³ B( f ' ) ¨©1  cos

I ( x)

f

2ʌ x f ' · ¸ d f '. c ¹

101

(4.50)

On the contrary, B ( f ) is deduced from the measured intensity by reverse transformation. 2 c

B( f )

L

³ >I ( x' )  I @ 0

L

§ 2ʌ x f ' · cos¨ ¸ d x' © c ¹

(4.51)

where I0

³ B( f ' ) d f ' .

(4.52)

f

In order to convert B ( f ) back to transmission, it must be corrected by the contribution of the light source. This can be done with the measurement of the interference pattern without a sample. At the same time, this procedure eliminates the effects that originate from the atmosphere. Electron beam induced current (EBIC) and light beam induced current (LBIC). A total surface p-n junction, for instance, a solar cell with a thin emitter, is assumed. The junction is reversed biased for EBIC and short-circuited for LBIC. If an electron beam or a light beam impinges on the junction, the device works as a photodetector (EBIC) or as a solar cell (LBIC). Since the beams are closely bundled compared to the wafer diameter, the measured current can be regarded as a measure of the lateral homogeneity of the junction. When scanning the beam in x and y-directions, an image of the wafer is obtained. Figure 4.72 is an example of

Fig. 4.72

LBIC on a multicrystalline wafer

102

4 Nanolayers

the image of a multi-crystalline wafer [98]. The grain boundary is clearly visible as a valley. The Makyoh concept. A magic mirror, which the Japanese called Makyoh, is based on this concept. If one directly looks upon this mirror nothing can be observed. When sunlight is reflected from its front onto a wall, however, the image of a feature appears on that wall. This feature is engraved on the mirror’s back (Fig. 4.73). Visible light is bundled parallelly and directed on the wafer surface to be measured. There, it is reflected and subsequently detected with a CCD camera (Fig. 4.73a). It should be noted that the wafer is held at a certain distance so that the reflected image is outside of the image plane. This shows the latent picture (in our case, a concavity). Concavities appear bright, convexities dark (Fig. 4.73b). Some examples are shown in Fig. 4.74.

Fig. 4.73

Makyoh reflection: (a) Experimental system, (b) principle of reflection [99]

(a)

(b)

(c)

Fig. 4.74 Optical inspection of wafer surfaces. (a) Defect-free wafer, (b) wafer with hills and saw marks, (c) wafer with warpage and local waves after As implantation [99]

4.3 Applications of Nanolayers

4.3

103

Applications of Nanolayers

Among the three nanostructures nanodefects, nanolayers and nanoparticle, the nanolayers have found the most widespread applications. They are mostly used for electronic or protective purposes: x x x x x x x x x x x x x x x

MOS gate oxide Field oxide SOI oxide Amorphous layers for heterojunction solar cells, TFTs, optical sensors MOS channels Counter-doped Si layers for p-n junctions, transistors Recrystallized layers on dielectrics for device production Oxide as implantation and diffusion masks Oxide for the photolithography Silicides or metals for connections Epitaxial layers for transistors, laser, quantum detectors ITO for anti-reflection and charge collection in solar cells Back side surface field (BSF) layers in solar cells Metal layers for glasses, lenses, beam splitters, interferometers Anti-corrosion and passive layers

This enumeration is by no means complete, and each item can be subdivided into numerous applications. For instance, counter-doped layers produced by ion implantation are used for MOS source and drain, CMOS wells, isolation in integrated circuits, buried channel CCDs, layers for the suppression of blooming in the CCD, emitter for solar cells, etc. The number of applications in corrosion and metallization is vast as well. Epitaxial layers enable the production of high frequency, opto-electronic, and quantum layer devices.

4.4

Evaluation and Future Prospects

Historically, the development of thin layers began early and has prospered greatly. Nevertheless, it is afflicted with some problems which will have to be dealt with in future research. In the following, some examples are briefly described: (i) The scaling and reduction of all geometrical sizes of electronic devices has also lead to the application of thinner gate oxide. It has to be considered, though, that a substantial aspect of gate oxide based MOS technique is based on its high isolation ability. However, when thickness falls short of 4 nm, tunneling currents removing the blocking capability come into action. The only remedy so far consists of accepting these tunneling currents and simply refreshing the signals. So far it is an unsettled question whether more stable dielectrics can be developed. (ii) The same question refers to the operability of image-delivering CCD devices on the basis of isolation oxides. In this case the signal (the accumulated

104

4 Nanolayers

charge) can flow over the oxide as tunneling current. Thus, apparently the necessary refreshment times are increased but the signal is nonlinearly falsified. (iii) When dealing with thinner oxides, the above field eventually increases. Effects such as oxide charge trapping and associated bias point shifts can occur then. Current blocking mechanisms such as Coulomb blockade, telegraph noise become apparent among other things. (iv) Contradictory demands are made concerning the desired size of the dielectric constants of insulators. On the one hand, capacitance values become increasingly small by reducing dimension. Thus, the desire for a high dielectric constant exists. On the other hand, electrical connections are packed more closely together so that the danger of cross talk increases. The capacitive cross-talk is almost proportional to the dielectric constant. Therefore, insulators with small dielectric constant should be used. (v) In the production of solar cells, antireflection coatings are used as outer layers. A good optical transparency and a small ohmic resistance are required. At present, a transparency of 92 % and a resistivity of 2·104 :cm are usual. Manufacturers are interested in better values and in a cheaper coating process in order to be able to increase the efficiency and to lower the price of the solar cell. (vi) A practically unresolved problem still exists in the structuring techniques. A substantial new procedure for this is discussed in Chap. 7. Here, it is only anticipated that it is not sufficient any longer to further develop conventional techniques (lithography, etching). Instead, some new solutions are appearing. An innovative procedure consists of tilting a nanolayer about 90° and using its thickness as a characteristic measure, for instance, for the drain-source separation (spacer technique). Another new procedure places individual atoms next to each other in order to form metallization lines. (vii) With increasing wafer sizes, inhomogeneities of the layers show to be a problem in signal electronics, power electronics, and also in solar cells. At the same time, problems occur in the detection technique. During deposition, for instance, a mapping representation, i.e. an image of the topography of a parameter of the deposited layer, is frequently required. With a lateral resolution of 10 µm, this can be extremely time-consuming in the case of a 12˝ wafer. (viii) With decreasing thickness of a series of thin layers manufactured by epitaxy or CVD, diffusion becomes a serious problem. (ix) A limiting factor in the efficiency of a processor is its communication with other parts of the system. According to Rent’s rule, the number of external connections Ni should reach at least Ni

2.5 N g

0.6

(4.53)

whereby Ng is the number of gates on the processor. For today’s chips, this number is not achieved by about an order of magnitude. Even with further progress in the structuring of metal layers, no improvement can be expected. On the contrary, the situation is worsened by the fact that with each reduction of the structures, the number of gates increases quadratically (with the surface) but the number of connections do so only linearly (with the edge length).

4.4 Evaluation and Future Prospects

105

A promising way out of this dilemma can be the application of free space optics. The electrical signal on a processor is converted into an optical signal and directed on a second chip facing the processor. From there, it is directed to the desired position in the processor by a lens system [100, 101]. Further advantages with this system are higher bandwidths and the reduction of power losses.

5

Nanoparticles

5.1

Fabrication of Nanoparticles

At first sight a nanoparticle is defined as a ball or a ball-like molecule which consists of a few 10 to some 10,000 atoms interconnected by interatomic forces but with little or no relationship to a solid state. However, this intuitive concept is not fulfilled in many cases. A first example is a nanocrystalline Si particle which is embedded into an amorphous matrix. Other examples are nanoparticles which are compressed to bulk ceramic or surface layers. It should be considered that deposited nanoparticle layers differ from uniform layers, particularly due to the presence of grain boundaries, which leads to different electrical and optical behavior.

5.1.1

Grinding with Iron Balls

First of all, a container is filled with stainless steel balls of a few millimeters in diameter. The material to be crushed is added in the form of a powder of about 50 µm diameter grain size. After filling the container with liquid nitrogen, a rotating shaft grinds the material. The grinding periods are within the range of minutes to some 100 hours. This process is simple; its weakness, however, lies in the fact that the grinding balls contribute to impurities.

5.1.2

Gas Condensation

A typical system is shown in Fig. 5.2. The operation occurs in an evacuated chamber with a pressure of 105 Pa. After mounting the raw material on one or more crucibles, it is evaporated thermally, by an electron gun, or by ion sputtering. The evaporated atoms or molecules unite and form particles of different sizes. Finally they are captured with a cold finger from which they are scraped off and collected with a funnel. The particle diameter is usually within the range of 5 to 15 nm.

5.1.3

Laser Ablation

The raw material is provided as a solid. Its dissolution is achieved by a focused laser beam—similar to the cutting of a metal or a semiconductor. The advantage

108

5 Nanoparticles

Fig. 5.1

Ball mill for the fabrication of nanoparticles [102]

Fig. 5.2

System for inert gas condensation of nanocrystalline powder [103]

of this procedure is a 1:1 transfer of the material composition from the raw material to the particles. The system has already been shown in Fig. 4.8. 5.1.4

Thermal and Ultrasonic Decomposition

As an example of thermal decomposition, the starting material iron pentacarbonyl, Fe(CO)5, is considered. It decomposes in a polymeric solution, e.g., polybutadi-

5.1 Fabrication of Nanoparticles

109

ene, and thus produces iron particles of 7 to 8 nm diameter. The material can also be decomposed as immersion in decane by ultrasonic irradiation, resulting in particle sizes roughly between 6 and 240 nm. Smaller values apply to the more highly solved systems. 5.1.5

Reduction Methods

Some metal compounds (e.g., chlorides) can be reduced to elementary metallic nanopowder by the application of NaBEt3H, LiBEt3H, and NaBH4, for example. The reaction equation can be written as (M: metal, Et: ethyl): MClx + x NaBEt3H ĺ M + x NaCl + x BEt3 +

5.1.6

1 2

x H2

(5.1)

Self-Assembly

This phenomenon is usually found in the heteroepitaxy. Three-dimensional islands are formed with a rather surprising regularity on a substrate. Due to the free surface energies (substrate–vacuum, substrate–film, film–vacuum), two extremes can occur: regular layer-on-layer growth and cluster formation. The first case is comparable with the picture of butter on bread, and the second one with water drops on butter. In the case of a large lattice mismatch, an intermediate case can occur. The film follows a layer-on-layer growth but develops greater and greater pressure. With sufficient film thickness the film will form three-dimensional islands as in the preceding second case (Stranski-Krastanov mechanism, Fig. 5.3). An example of these self-assembly islands is presented in Fig. 5.4. 5.1.7

Low-Pressure, Low-Temperature Plasma

Although plasma excitation can take place with direct or alternating current, normally a conventional capacitively coupled RF plasma device is used. A gas (e.g., silane) is let in so that a pressure of 1 to 200 Pa develops. As shown in Sect. 4.1.1, the gas is ionized by the applied field. The free electrons acquire kinetic energy

Fig. 5.3 Stranski-Krastanov growth [104]

110

5 Nanoparticles

Fig. 5.4

Self-assembled As0.5Ga0.5As islands on In0.2Ga0.8As [105]

and, in return, ionize neutral molecules upon impact. Due to their mass, the ions are slow and maintain the temperature of the gas. This justifies the name of lowtemperature plasma. In the applications described in Sect. 4.1.1, interest is focused on the deposited layers. Here, however, we are dealing with the ionized fragments of the gas which maintains the plasma. As an example, the fragments from silane after electron collision are listed in Table 5.1. These ions and their agglomerates form the nanoparticles which can then be examined. The particles produced are accumulated mainly close to the plasma layer of the power-operated electrode (this is a sign that the fragments are negatively charged), where they can be measured mostly in situ. After extinguishing the plasma, however, it is possible to collect some particles which had fallen onto the substrate. 5.1.8

Thermal High-Speed Spraying of Oxygen/Powder/Fuel

Thermal spraying is a procedure for nanocrystalline cover layers. A burn reaction produces high temperature and high pressure within a spray gun. The pressure Table 5.1

Dissociation products after impact of an electron with silane [106]

Products SiH2 + 2H + e SiH3 + H + e SiH + H2 + H + e Si + 2H2 + e SiH* + H2 + H + e Si* + 2H2 + e SiH2+ + H2 + 2e SiH3+ + H + 2e Si+ + 2H2 + 2e SiH+ + H2 + H + 2e SiH3 + H SiH2 + H2

Threshold energy, eV 8 (?) (?) 10 (?) 12 (?) 10.5 11.5 11.9 12.3 13.6 15.3 6.7 7.7

5.1 Fabrication of Nanoparticles

Fig. 5.5

111

Spray gun for thermal high-speed spraying of oxygen/powder/fuel [107]

drives particles of a nanopowder contained in the pistol through a nozzle onto the surface which is to be covered. An example of a spray gun is shown in Fig. 5.5. 5.1.9

Atom Optics

An atom beam which is produced by heating up a material in a crucible is assumed. The beam is bundled by one or more apertures and steered onto the substrate (Fig. 5.6). In the next step, the beam is subjected to the dipole forces of a standing wave which is produced by a laser beam (Fig. 5.7). The atoms will devi-

Fig. 5.6

Manufacture of an atom beam [108]

Fig. 5.7

Lens arrangement with a standing wave [108]

112

5 Nanoparticles

ate to the nodes of the standing wave where they are subjected to the smallest forces. The ideas of Fig. 5.6 and 5.7 can be combined for the assembly of atomic bundling (Fig. 5.8). A lattice pattern reflecting the wavelength of the laser is produced (Fig. 5.9). A second standing wave may be used perpendicularly to the first and to the direction of the beam. This gives rise to a two-dimensional pattern of deposited atoms (Fig. 5.10). 5.1.10 Sol Gels A sol (hydrosol) is a colloidal dispersion in liquid. A gel is a jelly-like substance formed by coagulation of a sol into a gel. The best known example of a sol gel process is probably the production of SiO2. A catalyst (acid or base) is added to a solution of tetramethoxysilane (TMOS), water, and methanol. Hydrolysis of the Si–OMe (Me: methyl) bonds

Fig. 5.8

Assembly for atom focusing in a standing wave [108]

1 µm

Fig. 5.9 AFM images of a one-dimensional lattice with 212 nm pitch and 38 nm line width formed by laser-focused atom deposition of chromium [109]

5.1 Fabrication of Nanoparticles

113

Fig. 5.10 AFM images of a two-dimensional lattice formed by laser-focused Cr deposition [110]

leads to the formation of Si–OH groups: Si(OMe)4 + 4H2O ĺ “Si(OH)4” + 4MeOH

(5.2)

Further dehydration reduces the “Si(OH)4” to SiO2 gel. If hydrolysis and condensation are completed, a silicon oxide xerogel is formed (in Greek, xeros means dry). During the reaction, the gel reaches a viscosity so low that it can be applied onto a centrifuge and distributed over the wafer. When annealing over 800 °C, homogeneous oxides, comparable to bad MOS gates, can be manufactured. If doped SiO2 layers are produced, they can be used as diffusion sources in a subsequent process. At moderate and low solidification temperatures, the procedure delivers the socalled nanocomposite. By definition, nanocomposites contain nanoparticles of less than 1000 nm in a host matrix. The following nanocomposites have already been manufactured (the list is not complete) [111]: nano-Co/Mo, Cu, Fe, Ni, Pd, Pt and Ru in Al2O3, SiO2, TiO2 and ZrO2 gels, nano-C, Cu/Ni, Pd/Ni, and Pt in silica gel, nano-Ag, Ge, Os, C, Fe, Mo, Pd, Pt, Re, Ru and PtSn in silica gel-xerogel. 5.1.11 Precipitation of Quantum Dots Quantum dots are three-dimensional semiconductor materials in or on a matrix. Nanocomposites from semiconductor materials and the above-mentioned selfassembled islands belong to this group. Sometimes it is difficult to differentiate between quantum dots and nanodefects. An example is SiO2 implanted with Ge, which is used for photoluminescence experiments (Sect. 3.3.4). The earliest descriptions of quantum dots took place with the investigation of semiconductor precipitation in glasses. Precipitation is still used in the manufacturing of CdS, CdSe, CdTe, GaAs, and Si nanocrystallites in silica glasses. The contaminants are added to the melt, and after a further annealing step from 600 to 1400 °C, they form precipitates of controllable size, for instance, 2 nm for CdTe dots in boron silicate glass. Another procedure is codeposition of quantum dots with thin films. There are several modifications, but the common principle is the production of nanocrystal-

114

5 Nanoparticles

lites in a separate step (by evaporating, laser ablation, sputtering a target, etc.). They are directed towards a substrate which is, however, covered at the same time with a film so that they are included into this film. Quantum dots can also be manufactured by means of lithography. Since a high resolution is required, electron beam lithography must be employed. The procedure takes place mostly in such a way that the material which is to be converted into quantum dots is deposited on a substrate like GaAs via MBE. The size of the electron beam spot determines the smallest possible size of the quantum dot. Therefore, if the wafer is etched, islands of this size remain. They are further reduced by etching so that quantum dots of a few 10 nm can be produced. Very often, the layers are covered in order to improve the results. 5.1.12 Other Procedures GaN nanoparticles were synthesized in autoclaves with the reaction of Li3N and GaCl3 in benzene at 280 °C. The particle size was approximately 32 nm [112]. The same material was obtained by pyrolysis of polymeric galliumimide, {Ga (NH3)3/2}n, in the presence of NH3 [113]. Fullerenes (Sect. 2.2) are acquired by arc discharge in plasma or by an atomic beam furnace (Fig. 5.6) filled with carbon. After dissolution of the soot particles in an organic liquid, the fullerenes can be separated by gas chromatography.

5.2

Characterization of Nanoparticles

5.2.1

Optical Measurements

Nanoparticles are more or less characterized in the same way as nanodefects or nanolayers. In their case, size effects are more apparent. Therefore, in view of Sect. 2.1, they are attractive, namely, to pursue the transition from the solid state to the nano-behavior. A first comparison is obtained from IR measurements of an a-Si:H film and silicon nanopowder (Fig. 5.11) [106]. Three bands appear, namely stretching bands, bending bands, and wagging bands. These bands can be assigned to specific groups of hydride and polymer chains, and their presence reveals information on the specific nanostructure. Please note the band between 840 and 910 nm [a proof of SiH2 and (SiH2)n], which is missing in a-Si:H. A similar comparison can be drawn from the luminescence spectra of bulk and nanocrystalline Si and the absorption spectra of bulk and nanocrystalline Ge (Fig. 5.12). Optical absorption measurements provide additional information about the development of the solid state parameters, depending on cluster size. An example is the measurement presented in Fig. 5.13 where optical density of CdSe vs. light energy is plotted [116]. The blue shift with reducing cluster size is a generally recognized phenomenon. However, we kindly refer the reader to the measurements in Sect. 2.3 [9] where the opposite behavior is described.

5.2 Characterization of Nanoparticles

Fig. 5.11

115

IR spectra of silicon nanopowder in comparison to a standard a-Si:H film

Fig. 5.12 (a) Cathodoluminescence spectra of nano and bulk Si [114], (b) dispersion of bulk Ge and absorption of nano Ge in an Al2O3 matrix [115]

5.2.2

Magnetic Measurements

The measurement of the ferromagnetism of nanosize iron and the comparison with bulk iron is shown in Fig. 5.14 [117]. It is clearly seen that the saturation behavior is lost with decreasing grain size. The authors explain this behavior as the transition from ferromagnetism to superparamagnetism. 5.2.3

Electrical Measurements

Only one example is shown here since electrical devices form a subsequent chapter of this work.

116

5 Nanoparticles

Fig. 5.13 Absorption spectrum of CdSe for numerous sizes of nanoclusters. The measurements are performed at 10 K.

Fig. 5.14 Saturation curves of nanosize iron and macroscopic iron powders. M is for the molecular concentration of the raw Fe(CO)5 solution in decane; the particle size decreases with reducing molecular fraction.

5.3 Applications of Nanoparticles

117

Due to the reduction of dimensions, the particles are subjected to a transformation of the band structure as shown in Sect. 2.3. This applies particularly to metal particles whose electrons can be thought to be locked up in a box with high walls where standing waves develop as eigenfunctions. Such a system can controllably exchange single electrons with a second one by tunneling through the walls. The physics of current transport will be discussed later. However, the measurement setup and the arising I-V curves of the so-called ligand-stabilized Au55 cluster (the ligand is a colloidal chemical stabilizer) are already depicted in Figs. 5.15 and 5.16, respectively.

5.3

Applications of Nanoparticles

Nanoparticles are already applied as: x

Optical filters in sunscreen and skin cream

Fig. 5.15 STM as a tool for the measurement of single electrons at a ligand-stabilized Pt309 nanocluster [118]

Fig. 5.16

I-V curves for a ligand-stabilized Au55 cluster [118]

118

5 Nanoparticles

x x x

Dirt repellents for cars and windows, Fig. 5.17 [119] Flat screens, Fig. 5.18 [120] Single electron transistors

Research is underway in the area of x x x x x

Nanowheels, nanogears, nanofilters Drug pumps located in the human body, long-term depots Luminescent devices (after installation in zeolites) Energy storage (hydrogen in zeolites) Electronic devices

The following applications are expected particularly for the fullerenes: x x x x x x x x x x x x x x x x

Particle absorption filters for cigarettes Chromatography Molecular containers Sensor cover layers for surface wave devices Additives in fuels Lubricants Catalysts for hydrogenation Photocatalysts for the production of atomic oxygen in laser therapy Production of artificial diamonds Functional polymers, photoconductive films Alkali metal MC60 chain formation (linear conductivity) Superconductivity (doping with alkali metals) Ion engines Raw material for AIDS drugs Tools that are harder than diamond Nanoelectronic devices

Again, the enumeration is incomplete.

5.4

Evaluation and Future Prospects

In order to evaluate the progress in the area of nanoparticles, we quote literally from a publication on the nanoparticle industry’s total revenue [106]. Based on these figures, we may draw a conclusion on the future development with due caution. The quotation reads: “According to the technical-market study ‘Opportunities in Nanostructured materials’, published recently by the Business Communications Co, the overall U.S. market for nanostructured particles and coatings was valued at an estimated 42.3 million US$ for 1996. This tabulation included ceramic, metallic, semiconducting, and diamond nanostructured materials produced in commercial quantities with the exception of nanoscale amorphous silica powder, which commands a market of several hundred million dollars. The market for nanostructured materials is projected to grow about 400 % in 5 years. It is expected to

5.4 Evaluation and Future Prospects

Fig. 5.17

Partial coverage of a car door with a layer of nanoparticles for dirt rejection

Fig. 5.18

Flat screen from nanotubes

Table 5.2

Overall U.S. markets for nanostructured materials

1996 US$ (Mio) % Particlesa 41.3 97.6 Coatings 1.0 2.4 Total 42.3 100 a Dry powders and liquid dispersion

2001 US$ (Mio) 148.6 6.0 154.6

% 96.1 3.9 100

119

Average annual growth rate, % 29.2 43.1 29.6

reach $154.6 million in 2001, corresponding to an average annual growth rate of 29.6 % from 1996 to 2001.”

Table 5.2 sums the overall U.S. markets for nanostructured materials. It should be noted that coatings obviously represent layers which contain nanoparticles (an example would be vapor-deposited fullerenes). Moreover, nanostructured materials can be equated with nanoparticles. According to unpublished sources, these figures were exceeded by far.

6

Selected Solid States with Nanocrystalline Structures

6.1

Nanocrystalline Silicon

6.1.1

Production of Nanocrystalline Silicon

Silicon with nanoscale crystalline grains—ranging in size from a few nanometers to 1000 nm—is referred to as nanocrystalline silicon (nano Si, n-Si). This form of silicon is usually composed of deposited layers of approximately 1 µm thickness each. On the contrary, when exceeding 1000 nm in grain size, we enter the domain of microcrystalline silicon. In this paragraph, production and analysis of nanocrystalline silicon are discussed, essentially based on [121]. It can be manufactured using different deposition methods such as x x x x x x x x

Electron cyclotron resonance CVD (ECRCVD) [122], Photo CVD [123], Magnetron plasma CVD [124], Plasma-enhanced CVD (PECVD) [125, 126], Remote plasma-enhanced CVD [127], Hydrogen radical CVD [128], Spontaneous CVD [129], and Reactive sputtering [130, 131].

In the following, emphasis is put on the PECVD procedure (cf. Sect. 5.4), which is done very similarly to the deposition of amorphous silicon. As a major difference, however, higher frequencies (e.g., 110 MHz) are preferred during nanocrystalline deposition instead of the usual 13.56 MHz. While being helpful for the production of films, this measure causes a problem regarding homogeneity: with 13.56 MHz the wavelength is 22 m, and it shortens to 2.7 m with 110 MHz. Thus, it lies within the limits of the chamber size and standing waves can develop. Consequently, precautions must be taken for large-surface deposition with frequencies above 60 MHz. For instance, by a multi-point feed of the HF power with same amplitude and phase, the homogeneity of the HF potential and hence the deposition process can be improved. The raw material for the production of silicon layers is usually silane (SiH4). For the deposition of doped layers, phosphine (PH3) for n-type layers and diborane (B2H6) or trimethylborane [B(CH3)3] for p-type layers is added to the silane. Silane is a pyrolytic gas which reacts explosively with air or water vapor.

122

6 Selected Solid States with Nanocrystalline Structures

The massive dilution of the silane with hydrogen makes the second major difference. Contrary to argon or helium, this is a reactive dilution gas in the plasma which is able to react and intercept with radicals being detrimental for the layer deposition. Hydrogen can also restrict deposition and etch silicon. Investigations of hydrogen-diluted silane in connection with the deposition of a-Si:H have already been undertaken earlier by Chaudhuri et al. [132] and Shirafuji et al. [133]. There, the aspect of the degree of hydrogen dilution was not considered sufficiently. With a dilution R = [SiH4] / [H2] of >0.05, a-Si:H is formed using PECVD deposition, and this stability field with reference to the structural and electrical characteristics can be further subdivided. The positive effect on a-Si:H is the reduction of (SiH2)n chains. Furthermore, the density of the crystalline silicon increases up to 90 %, the refractive index increases, and the total hydrogen quantity built up in the structure decreases [134]. A strong dilution of the starting gas, silane, during plasma deposition can modify the structure of the deposited film from a pure amorphous to a mixture of amorphous and crystalline phases. Generally, nanocrystalline silicon is deposited under strong dilution of the silane with hydrogen (ratio 1:100–10,000) and under depletion of silane [135]. In the VHF range, nanocrystalline growth for a silane dilution of 1 can be achieved. In state-of-the-art quantum cascade lasers, the basic units are repeated between 20 and 40 times [329]. Despite the operating principle being similar, the quantum cascade laser exhibits a substantially more complicated structure in comparison to the quantum well infrared photodetector (QWIP) [330]. This difference is explained by an additional condition necessary for the operation of the laser: the population inversion between the two energy levels. Thus, the higher energy level must have a higher electron concentration than the lower level. In principle, the operation of the laser can be described with the help of the conduction band profile of a basic unit of this laser (Fig. 9.6) [331]. In the case illustrated, the barriers are made of AlInAs layers, and the quantum wells consist of GaInAs. Electrons tunnel from the injector into the electronic level E3 and fall on level E2 by sending out light quanta with

220

9 Innovative Electronic Devices Based on Nanostructures

Fig. 9.6 Conduction band profile in the area of the active layer of a quantum cascade laser (from [331])

Q = (E3 – E2) / h, followed by a non-radiative transition from energy level E2 to level E1. To achieve population inversion and laser operation, the electron tunneling rate from the two levels E2 and E1 into the neighboring conduction band must be higher than the tunneling rate from the level E3. Therefore, an electronic Bragg reflector consisting of a semiconductor superlattice is inserted into the QCL structure behind the active layer. This structure is depicted in Fig. 9.7a. The probability of transmission of the Bragg reflector’s electrons as a function of the energy position relative to the conduction band minimum can be seen in Fig. 9.7b [332]. As can be clearly seen, a forbidden band (mini-gap) develops and takes effect within the energy region of the level E3. The tunneling probability from the level E3 is two orders of magnitude lower than from the levels E2 and E1, whose energies correspond to the energy region of the mini-band in the Bragg reflector section of the laser. Thus, the necessary condition for population inversion is ensured. The first quantum cascade laser ever devised achieved a few mW optical power at cryogenic temperatures under pulsed operation conditions. As an example of these early QCLs, the emission spectrum and the emitted power as a function of the laser current of an InGaAs/InAlAs Fabry-Perot quantum cascade laser with an emission wavelength around 4.5 Pm are depicted in Fig. 9.8 [332]. An overview of the current developments concerning the optical power and the covered wavelength range of quantum cascade lasers is given in Table 9.2. At present, an emitted optical power of more than 1 W near room temperature [335]

9.3 Quantum Cascade Laser

221

(a)

(b)

Fig. 9.7 Schematic representation (a) of a period of the quantum cascade laser and (b) energy dependent transmission probability for electrons of the Bragg mirror (from [332])

Fig. 9.8 Optical power as a function of laser current and optical emission spectrum of a Fabry-Perot InGaAs/AlInAs quantum cascade laser (from [332])

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9 Innovative Electronic Devices Based on Nanostructures

and of up to 6 W at a temperature of 80 K [333] have been achieved under pulsed operation. It is also interesting to note that a wavelength range from 3.8 up to 24 Pm can be covered with QCLs using only three different combinations of active layer materials. For example, this wavelength range is interesting for optical data transmission within the earth’s atmosphere, where there are optimal transmission conditions in the two spectral range windows from 3.5 to 4 Pm and from 8 to 10 Pm. It should be noted that the full infrared spectral range can be covered with III-V compound semiconductor lasers. Conventional semiconductor lasers based on electron-hole recombination cover the wavelength range up to 3.25 Pm [345], while QCL lasers cover the longer wavelength range. Besides the Fabry-Perot (FP) type lasers, also distributed feedback (DFB) quantum cascade lasers are developed today. Due to their narrower emission spectrum, these are better suited for spectroscopic and data transmission applications. In Fig. 9.9, the optical powerlaser current characteristics and the optical emission spectrum of a DFB InGaAs/

Table 9.2

Optical powers and wavelength ranges of quantum cascade lasers

First author (Year)

Active layer material

Yang et al. [333] InAs/GaInSb/ (2002) AlSb Yang et al. [334] GaInAs/AlInAs (2002)

Electronic (optical) structure MQW (Fabry-Perot) MQW (Fabry-Perot)

Hofstetter et al. GaInAs/AlInAs [335] (2001) Scamarcio et al. GaInAs/AlInAs [336] (1997)

undotiertes SL (DFB) MQW (Fabry-Perot)

Faist et al. [337] (2000) Page et al. [338] (1999) Hofstetter et al. [339] (1999) Tredicucci et al. [340] Anders et al. [341] (2002) Rochat et al. [342] (2001)

nipi SL (Fabry-Perot) MQW (Fabry-Perot) MQW (DFB) MQW (Fabry-Perot) MQW (Fabry-Perot) chirped SL (Fabry-Perot)

GaInAs/AlInAs GaAs/AlGaAs GaInAs/AlInAs GaInAs/AlInAs GaAs/AlGaAs GaInAs/AlInAs

Colombelli et al. GaInAs/AlInAs [343] (2001) Colombelli et al. GaInAs/AlInAs [344] (2001)

undoped SL (Fabry-Perot) undoped SL (Fabry-Perot)

Max. optical power (at temperature) pulsed 6 W (80 K) pulsed 1 W (150 K) pulsed 900 mW (77 K), pulsed 240 mW (300 K) pulsed 1,15 W (273 K) pulsed 92 mW (393 K) pulsed 750 mW (80 K) pulsed 200 mW (210 K)

Emission wavelength, Pm 3.8 5.0

5.3 8.0

8.8 pulsed >1 W (77 K)

9.7

pulsed 80 mW (300 K) 10.2 CW 75 mW (25 K) CW 8 mW (80 K) pulsed 75 mW (78 K) pulsed 2 mW (300 K) pulsed 400 mW (210 K) pulsed 150 mW (300 K) pulsed 14 mW (70 K)

11.1

16.0

pulsed 3 mW (70 K)

24.0

12.6

19.0

9.3 Quantum Cascade Laser

223

AlInAs quantum cascade laser are depicted. At room temperature, this laser emits around 7.8 Pm with an optical power of up to 10 mW [346]. Furthermore, the emission wavelength can be tuned between 7.75 and 7.85 Pm by varying the temperature from 100 to 300 K, which is of interest to laser spectroscopy. For quantum cascade lasers with emission wavelengths below 4 Pm, InAs/ GaInSb/AlSb is preferred as active layer material [333]. With regard to the type of the electronic structure, nipi-superlattices (layer sequence of n-type, intrinsic, ptype, intrinsic) [337] or intrinsic superlattices [335, 343, 344] have been used as the active layer of QCLs, besides the widespread multi-quantum-well (MQW). Thus, lasers with a high optical power in the spectral range around 5 Pm [335] and lasers with emission wavelengths up to 24 Pm [344] have been developed. Recently the production of GaAs/GaAlAs quantum cascade lasers with emission at wavelengths between 100 and 200 Pm has been reported [347, 348, 349]. These monochromatic Terahertz emitters close the gap between electronic and optical oscillators in this wavelength range. Terahertz emission has interesting applications in biomedical imaging [350]. As shown in Fig. 9.10, a QCL with an emission frequency of 4.44 THz and a power of more than 2 mW has been reported [348]. This is a much higher value of the emitted power as compared to

(a)

(b)

Fig. 9.9 (a) Optical power as a function of laser current. Inset: temperature dependence of the lasing threshold current density. (b) Temperature dependence of the emission wavelength of a distributed feedback InGaAs/AlInAs quantum cascade laser. Inset: optical emission spectra for different temperatures between 77 and 300 K (from [346])

224

9 Innovative Electronic Devices Based on Nanostructures

pure electronic Terahertz generation using harmonic generation. It should be mentioned, however, that for broadband Terahertz generation using relativistic electrons in a particle accelerator emission powers greater than 20 W have been reported [351]. First results with regard to electroluminescence in Si/SiGe cascade emitters [352] offer a good chance of manufacturing of silicon based quantum cascade lasers in the future [353]. 9.3.2

Quantum Cascade Lasers in Sensing and Ultrafast Free Space Communication Applications

Due to the short electron lifetime, the quantum cascade laser is an optical emitter that can be—in principle—modulated very fast. Thus, theoretical modulating frequencies higher than 100 GHz can be achieved. These frequencies are higher than those of lasers used in optical fiber communication systems at wavelengths of 1300 or 1550 nm. In first data transfer experiments, data rates of up to 5 Gb / s have been achieved using QCLs but still over short distances of maximum 350 m [354, 355, 356]. A further interesting application for lasers with emission in the far infrared is the trace analysis of gases in the atmosphere. For this application, a tunable monomode laser is needed, like the DFB quantum cascade lasers. Methane, nitrogen oxide, ethanol, and the different isotopes of water have been detected in ambient air by means of a sensing system using a quantum cascade laser as emitter and a mercury cadmium telluride (MCT) detector as receiver [357]. In a further step, there is interest in replacing the MCT detector with a quantum well infrared

Fig. 9.10 Optical emission spectra of a Terahertz Fabry-Perot GaAs/GaAlAs quantum cascade laser for various laser currents (from [348])

9.4 Single Electron Transistor

225

photodetector, using the same material system as for the production of the quantum cascade laser, and possibly to integrate emitter and detector on the same chip. Another alternative would be to use the QCL itself as photodetector. This functionality has already been demonstrated [358].

9.4

Single Electron Transistor

9.4.1

Operating Principle

The single electron transistor (SET) is an example of an electronic device where a final limit of electronics has already been reached: the switching of a current carried by just one electron. The operating principle can be understood with the help of Fig. 9.11 [359]. In principle, the SET consists of two tunnel contacts with associated capacitances (Cs and Cd) and an intermediate island to which an operation voltage (Vg) is capacitively coupled via Cg. By varying Vg, the electrical potential of the island can be changed. An insulator being embedded between two electrical conductors or semiconductors partly loses its insulating characteristics for a layer thickness which is in the lower nanometer range (about 5 nm) due to charge carrier tunneling. Thus, the probability of the transmission of charge carriers increases exponentially with decreasing thickness of the insulator layer. On the one hand, this quantum mechanical effect limits the further miniaturization of the classical MOS transistor due to increasing gate oxide leakage. This leads particularly to stability problems due to the charge carrier capture within the gate oxide and thus to a nontolerable displacement of the transistor characteristics during prolonged operation. On the other hand, this tunneling current enables the operation of the single electron transistor. Besides the capacitances Cs and Cd, electrical conductivities 1 / Rs and 1 / Rd can also be associated with the two tunnel contacts due to the tunneling current. Under which circumstances will a current flow between drain and source if an external voltage Vd is applied between these contacts? Let us assume that there are already n electrons on the island. One further electron can tunnel through the left barrier, if it has a charge energy of

Fig. 9.11 Schematic representation of the double barrier structure of a single electron transistor (from [359])

226

9 Innovative Electronic Devices Based on Nanostructures

(n  1)

e2 2(C s  Cd  C g )

(9.1)

At the same time, this electron gains energy ('E) by its transfer from the left electrode to the island due to the energy difference between these two points: 'E

e

Vd C s  Vg C g Cs  Cd  C g





Therefore, the electron will only arrive on the island if the total energy difference is negative. In the opposite case, a coulomb blockade is given which can only be overcome by a further increase of the applied voltage Vd. A possible implementation of a SET is shown in Fig. 9.12. The basic element is an ultrathin silicon-oninsulator (SOI) film. Thickness modulation due to anisotropic etching of the center part of the SOI film results in the formation of a series of quantum dots [360]. The gate contact is formed by polysilicon deposition on the upper oxide layer. The resulting current-voltage characteristics of such a device are presented in Fig. 9.13. As can be seen, characteristic levels are formed with constant gate voltage and varying Vd (Fig. 9.13a), while the SET current oscillates at a constant voltage Vd and a varying gate voltage (Fig. 9.13b). This oscillation can be explained by the fact that tunneling from the right contact to the island during increasing gate voltage is also possible and the transistor is again switched into the blocking state. This process is repeated by further increasing the gate voltage and leads to the observed oscillations of the electrical current. The plots presented in Fig. 9.13 have been taken at room temperature. As a condition for the operation of the SET, the charge energy EC

e2 2(C s  Cd  C g )

(9.3)

should be larger than the thermal energy k T. This means that the maximum operating temperature decreases linearly with increasing device capacitance. While a capacitance of about 1 aF is tolerable at room temperature, this value rises to

Fig. 9.12

Schematics of a SOI technology based single electron transistor (from [360])

9.4 Single Electron Transistor

(a)

227

(b)

Fig. 9.13 Current of a SET measured at room temperature (a) as a function of the applied drain-source voltage and (b) as a function of the applied gate-source voltage (from [360])

about 60 aF at 4.2 K. Ie., the smaller the device dimensions and thus the electrical capacitances, the higher the maximum allowed operating temperature. 9.4.2

Technology

Listing all technologies used today for the fabrication of single electron transistors would be beyond the scope of this book. Instead some structures which have been implemented so far are specified in Table 9.3 by naming the used island and barrier materials and the respective manufacturing methods. The more interested reader is kindly referred to the indicated quotations where these technologies are described in more detail. At the same time, a characteristic energy Ea is listed in this table. As a rule of thumb, it should be considered that the maximum allowed operating temperature (T) can be estimated from the relation: Table 9.3

Data on selected single electron transistor technologies

Materials (Island; Barrier) Al; AlOx CdSe; Organic Al; AlOx Ti; Si Carboran molecule Si; SiO2 Nb; NbOx

Fabrication methods Evaporation by means of an e-beam produced mask Nanocrystal bond to structured gold electrodes Evaporation on a structured Si3N4 membrane Metal evaporation on a structured Si substrate E-beam structured thin layer gate + STM electrode E-beam structuring + oxidation on SIMOX layer Anodic oxidation by means of STM

Ea, meV

Reference

23

[363]

60

[364]

92

[365]

120

[366]

130

[367]

150

[368]

1000

[369]

228

9 Innovative Electronic Devices Based on Nanostructures

kT 

Ea 10

(9.4)

with k being the Boltzmann constant. As can be seen, mostly metal/metal oxide and semiconductor/insulator systems are used for the fabrication of SETs. The growing use of organic layers and molecules is also remarkable. Regarding SET manufacturing, evaporation techniques using electron-beam structured masks and structuring with the scanning tunneling microscope (STM) are predominant. Single electron transistors have been fabricated using superconducting Nb/Al structures with AlOx barriers [369], self-organized growth of GaN quantum dots [370] or Co nanoparticles [371]. The most advanced SETs, however, are devices manufactured by classical microstructuration techniques and based on silicon or III-V semiconductor technology. Coulomb blockade oscillations have been observed in multi-gate SET structures using GaAs/InGaAs/AlGaAs [372] or AlGaAs/GaAs/AlGaAs [373] as semiconductors. Integrated structures of more than one SET have already been produced using silicon nanostructures. As an example, the production of a SET employing the socalled PADOX technique is illustrated in Fig. 9.14. This technique is based on the thermal oxidation of silicon quantum wires with a trench structure. It has enabled the fabrication of pairs of single electron transistors with good reproducibility. As a first step toward more complex integrated SET circuits, this technology has also enabled the production of simple inverters, working at a temperature of 27 K [374]. The idea of Coulomb blockade based devices is not limited to single electron transistors, but can be extended to hole transport based devices. This has been

Fig. 9.14 Principle of SET fabrication based on the PADOX and V-PADOX technology (from [374])

9.4 Single Electron Transistor

229

Fig. 9.15 Atomic force microscope image of a diamond single hole transistor (from [375])

demonstrated by the manufacturing of a single hole transistor (SHT) based on the modification of a hydrogen terminated diamond surface by means of an atomic force microscope (AFM). An AFM image of such a transistor is depicted in Fig. 9.15. The bright local oxidized regions can clearly be distinguished from the dark, hydrogen terminated regions (including the SHT island). This SHT showed the typical Coulomb oscillations of the drain current with variations of the gate voltage at a temperature of 77 K. 9.4.3

Applications

The main fields of application of the single electron transistor are sensor technology, digital electronic circuits, and mass storage. As already shown in the preceding section, the SET reacts extremely sensitively to variations of the gate voltage Vg if the voltage Vd is adjusted as Coulomb blockade voltage, so that an obvious application is a highly sensitive electrometer [361]. As already mentioned, the Coulomb blockade is only effective if the thermal energy is lower than the charge energy of the island. Therefore, the differential electrical conductivity within this area is also a measure for the ambient temperature and enables the use of the SET as a temperature probe, particularly in the range of very low temperatures [376]. Moreover, the SET is a suitable measurement setup for single electron spectroscopy. For this purpose, the island of the SET structure, for instance, can be taken as an individual quantum point. Apart from the applications as sensors, further application as direct current normal is interesting. Since exactly one electron is transported in each period when applying an alternating voltage of suitable amplitude to the gate of the SET, the current between source and drain which flows through a single electron transistor is directly proportional to the frequency of the applied alternating voltage Vg. Since frequencies can be measured with high accuracy, a precise direct current measurement standard can thus be implemented [377].

230

9 Innovative Electronic Devices Based on Nanostructures

Fig. 9.16

(a) Principle and (b) implementation of a SET-FET hybrid circuit (from [361])

The application of the SET as a switch and memory in digital electronics, operating at room temperature, has found great interest. However, there are some prin-

9.4 Single Electron Transistor

231

cipal problems: as stated earlier, the operation of a single electron transistors at room temperature requires extremely small island capacities of about 1 aF and thus structure widths around 1 nm. Today, this can be achieved in single structures, but the technology necessary for the production of complex digital circuits with these dimensions is not yet mature. Furthermore, there is a tradeoff between the operation of a SET at room temperature and the operation at higher frequencies. Very low device capacitances are obtained with small dimensions, but the electrical resistances associated with the tunneling barriers increase and reach values in the M: range. As a result, the critical frequencies of the SET are limited by relatively large RC constants. Despite all these difficulties, a variety of digital logic functions, including AND and NOR gates, has been obtained with the SOI technology based single electron transistor operating at room temperature (Fig. 9.11). The potential use of the SET as electronic mass memory has been discussed previously. Here, the number of electrons on a neighboring conducting island containing the stored information could be queried by means of a SET. Memory densities around 1012 bit / cm2 could be reached, which is some orders of magnitude higher than the values achieved by MOS memories today. The main problem consists in disturbing background charges, for example caused by charged impurities in insulating layers, which may induce mirror charges on the island of the SET [378]. Two different concepts to use the SET for data storage should be mentioned: in the first concept—a SET-FET hybrid approach—up to 100 SET based memory cells are read out by a field effect transistor (FET) based amplifier [361]. This type of memory requires—similar to the conventional DRAM operation—a refreshing of the memory content after each reading. It has been estimated that this approach can give memory densities up to 100 Gbit / cm2 at room temperature. The recording procedure, using a Fowler-Nordheim type tunneling with a typical delay time of approximately 10 ns, is relatively slow. The functionality can therefore be compared to that of an EEPROM. An illustration of the SET-FET hybrid concept is shown in Fig. 9.16 [361]. It is interesting to note that this type of memory is not sensitive to background charges and requires structure lengths of about 3 nm. In the second concept, it has been suggested that today’s dominating magnetic recording technique could be replaced by electrostatic storage (ESTOR) [361]. As presented in Fig. 9.17, the information is kept in loaded grains in a memory layer separated by means of tunnel barriers and a metallic layer from an insulating substrate. The process of writing and reading takes place by using a head floating about 30 nm over the surface with the island of the SET at the top. Memory densities of approximately 1 Tbit / inch2 are expected. This would be about 30 times higher than the theoretical limit calculated for magnetic memories. Similar memory densities have been estimated for the “Millipede” memory, based on a thermomechanical data storage concept that uses an atomic force microscope cantilever array to read and write a thin polymer film [380]. Similar to the case of the resonant tunneling diode, the SET is a good choice for multi-value logical circuits due to the periodical oscillations in the current-voltage characteristics. As an example for the implementation of such a device, the com-

232

9 Innovative Electronic Devices Based on Nanostructures

bination of a SET, fabricated with the already mentioned PADOX process, with a conventional MOSFET resulted in a complex current-voltage characteristics with multiple hysteresis [381]. This is one example that silicon based SETs are very attractive for digital applications because they can easily be interfaced to conventional electronics. As an example of an analog application of the single electron transistor, the fabrication of a radio frequency mixer has been reported that uses the nonlinear gate voltage-drain current characteristics of the SET for the fabrication of a homodyne receiver operating at frequencies between 10 and 300 MHz [382].

9.5

Carbon Nanotube Devices

9.5.1

Structure and Technology

The nanoelectronic devices presented so far are based on the “classical” materials—silicon and III-V compounds. In this chapter we present recent results on carbon nanotube (CNT) based devices that combine new developments in material science with innovative nanostructuring techniques. As demonstrated in Fig. 9.18, carbon nanotubes are made out of a network with the basic unit being six carbon atoms in ring configuration and arranged in form of cylinders. The electronic structure of the carbon nanotubes as represented by the band diagrams in Fig. 9.18

Fig. 9.17 Concept circuit of a writing/reading head for the electrostatic information storage by means of a SET (from [361])

9.5 Carbon Nanotube Devices

233

Fig. 9.18 Structure and electronic band diagram of metallic and semiconducting carbon nanotubes (from [383]). Note the different orientation of the rings.

critically depends on the geometry of the interconnection between the carbon rings, resulting either in metallic or in semiconducting behavior [383]. The growth of the cylinders with diameters in the nanoscale range is generally induced by the use of catalytic elements such as iron, molybdenum, and cobalt. The most common growth techniques are arc-discharge [384, 385], laser-assisted deposition [386], and plasma-enhanced chemical vapor deposition (PECVD), using a methane plasma at relatively high temperatures [387]. Depending on the growth parameters, the deposition processes result either in the formation of multi wall nanotubes (MWNTs) or single wall nanotubes (SWNTs) [383]. The particular interest in this new material is due to reports of very low specific resistivities for metallic carbon nanotubes [388] and on high hole mobilities for semiconducting nanotubes [383, 389]. The low density of surface states can physically explain these interesting electronic properties. The material forms a two-dimensional network of carbon atoms without the presence of dangling bonds. When assembling in cylindrical form the problem of the usually enhanced recombination at the edges of the semiconductor can be avoided [383]. First applications of metallic CNTs are wiring of microelectronic circuits and the use as field emitters for high resolution flat panel displays. As an example of the latter application, the manufacturing of a gated 3×3 field emitter cathode array (FEA) [390] is depicted in Fig. 9.19. A silicon surface is covered with a 1-nm thick iron layer as catalyst on top of a 10-nm thick aluminum layer and subsequently with a SiO2 layer. After deposition of the molybdenum gate electrode and the opening of the single cathode windows by reactive ion etching, metallic multi wall carbon nanotubes are grown on top of the Al/Fe metallization as cathode electrodes using a CVD process with an acetylene plasma at 900 °C. To give an idea of the dimensions of the device: the lengths of the white marks are 50 µm in Fig. 9.19g and 2 µm in Fig. 9.19h.

234

g)

9 Innovative Electronic Devices Based on Nanostructures

(h)

Fig. 9.19 Fabrication process and SEM images of a carbon nanotube based gated field emitter array (from [390])

9.5.2

Carbon Nanotube Transistors

The above-mentioned very high values of the charge carrier mobilities in semiconducting carbon nanotubes together with the small device dimensions make CNT based devices very interesting for microelectronic applications. So far field effect type transistors have mostly been implemented [389, 390, 391] because carbon nanotubes exhibit very high hole mobilities in particular. It should, however, also be mentioned that first experiments to realize a bipolar p-n-p transistor were successful [393].

Fig. 9.20 (a) AFM image, (b) schematic structure, and band diagrams without (c) and with (d) applied source-drain voltage of a TUBEFET (from [389])

9.5 Carbon Nanotube Devices

235

In Fig. 9.20, the structure and the atomic force microscope (AFM) image of a so-called TUBEFET are shown. On a silicon wafer covered with a thermal SiO2 layer, that serve as backside gate and gate insulator respectively, platinum (Pt) electrodes are deposited that form the source and drain contact. Subsequently the single wall carbon nanotubes are deposited or grown connecting the two platinum contacts. The room temperature characteristics of this TUBEFET are illustrated in Fig. 9.21. For positive voltages applied between drain and source contact, a clear threshold voltage for conduction has been observed whose value increases with increasing gate voltage. For negative voltages applied between drain and source, ohmic behavior has been found. Furthermore it can be seen that a 10 V change of the gate voltage results in a variation of the channel conductance of more than six orders of magnitude. One of the main problems regarding the fabrication of integrated circuits using CNT transistors is the limited reproducibility of the CNT growth process. An alternative approach to lateral integration is the manufacturing of arrays of CNTs based on vertical structures. Very homogeneous and reproducible growth of vertical CNT arrays by pyrolysis of acetylene on cobalt coated alumina substrates has been reported [394]. The structure and distribution of the diameters are shown in Fig. 9.22. The hexagonal cells, being open on top, have an average radius of 47 nm. They are positioned very symmetrically with an average distance of 98 nm. The manufacturing of vertical CNT transistors has already been reported [395]. However, they operated only at cryogenic temperatures of 4 K. The first successful integration of CNT field effect transistors has been done using lateral structures similar to the above-shown TUBEFET but with other materials [396]. A structure using gold drain and source contacts is shown in Fig. 9.23. In this case, an aluminum gate contact has been covered by a 100 nm thick

Fig. 9.21 Electrical device characteristics of a TUBEFET measured at 300 K. Inset: channel conductance vs. gate voltage (from [389])

236

9 Innovative Electronic Devices Based on Nanostructures

(a)

(b) Fig. 9.22 SEM image and histogram of the diameters of the nanotubes of a vertical carbon nanotube array (from [394])

Al2O3 layer as gate isolator. Both layers have been deposited on top of a SiO2 layer as substrate. The resulting enhancement-type p-channel MOSFETs with a voltage gain exceeding 10 have been wired together by gold metallization. In Fig. 9.24, the transfer characteristics of various digital functional circuits implemented by this technique are shown. Up to three interconnected transistors were used to implement an inverter, a NOR gate, a static RAM cell, and a ring-counter—with rather long switching times, however. As a perspective for other applications of carbon nanotubes for electronic devices, it should be mentioned that heterojunctions between CNTs and silicon quantum wires have already been reported [397]. In this case, the silicon quantum wires were grown by CVD deposition in a silane atmosphere selectively on top of the CNTs. They consisted of a crystalline core covered by a thin amorphous silicon layer and a SiO2 layer. The electrical characterization of this heterostructure showed a behavior similar to a Schottky diode and the current-voltage characteristics clearly exhibited rectifying behavior.

9.5 Carbon Nanotube Devices

(a)

237

(b)

(c) Fig. 9.23 (a) AFM image of a single SET, (b) schematic structure, and (c) AFM image of an integrated circuit structure using single wall carbon nanotube transistors (from [396])

Fig. 9.24 Circuit diagrams and measured transfer characteristics of integrated circuits produced with carbon nanotube p-MOS transistors (from [396])

References

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Historic Development 1. 2.

2

Semiconductor Industry Association (1999) The National Technology Roadmap for Semiconductors. San Jose (CA) Drexler KE, Peterson C, Pergamit G (1991) Unbounding the future: the nanotechnology revolution. Addison-Wesley, New York

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Clark T (1985) A Handbook of Computational Chemistry. Wiley & Sons, New York Pople JA, Beveridge DL (1970) Approximate Molecular Orbital Theory. McGraw-Hill, New York Deak P (1999) Approximate and parameterized quantum chemical methods for structural modeling of c-Si. In: Hull R (ed) Properties of Crystalline Silicon. Inspec, London, p 245 http://www.scientificamerican.com/exhibit/042897gear/042897nano.html (Status of 1997) Ghadiri R (1996) Molecular Engineering. In: Crandall BC (ed) Nanotechnology. The MIT Press, Cambridge (MA) Delley B, Steigmeier EF (1995) Size Dependency of Band Gaps in Silicon Nanostructures. Appl Phys Lett 67:2370 Maus M, Ganteför G, Eberhardt W (2000) The electronic structure and the band gap of nano-sized Si particles: competition between quantum confinement and surface reconstruction, Appl Phys A70:535 Kityk IV, Kassiba A, Tuesu K, Charpentier C, Ling Y, Makowska-Janusik M (2000) Vacancies in SiC nanopowders. Mat Sci Eng B77:147 Born M, Wolf E (1999) Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light. Cambridge Univ Press, 7th ed, Oxford. Liboff RL (1992) Introductory Quantum Mechanics. Addison-Wesley, 2nd ed, Reading von Klitzing K, Dorda G, Pepper M (1980) New Method for High Accuracy Determination of Fine-Structure Constant Based on Quantized Hall Resistance. Phys Rev Lett, vol 45, p 494 Pasquarello A, Hybertsen MS, Car R (1998) Interface Structure between Silicon and its Oxide by First-principles Molecular Dynamics. Nature, vol 396, p 58

240 15. 16. 17.

3

References Harrison RW (1999) Integrating Quantum and Molecular Dynamics. J Comp Chem, vol 20, p 1618 Car R (1996) Modeling Materials by ab-initio Molecular Dynamics. Kluwer Acad Publ, Norwell Wirth GI (1999) Mesoscopic Phenomena in Nanometer Scale MOS Devices. Ph. D. Thesis, University of Dortmund, Germany

Nanodefects 18. 19. 20. 21. 22.

23.

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27.

28. 29.

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Index

Major references are given in boldface type.

A Abbe diffraction condition 197 absorption 100 absorption spectrum – CdS cluster 136 – CdSe 116 – Ge 114 activation 55, 85 activation energy 28, 126 activation energy, nanopolishing of diamond 144 admittance bridge 64 AES ion excitation 86 Airy’s formula 66 AlCl3 as source material 203 aluminosilicate 129 analcime 129 annealing 18, 54 – thermal 179 AsS nanocluster 138 atom optics 111 atomic force microscopy 74, 128, 130, 195, 229, 231, 235 Auger electron emission 85 Auger electron spectroscopy 48, 86

B back side gettering 37 back side surface field 103 backscattering spectrum 96, 97 band gap – diamond 8 – GaAlAs 14 – GaAs 14, 214 – silicon 8, 10 – Sin clusters 8 band gap engineering 139, 183, 219 beam deflection, electrostatic 180

bending band 114 beveling 93, 143, 147 BF2 203 binding state 86 blade, surgical 150 blue shift 114, 138 BN 18 bonds – dangling 6, 233 – Si-H 19 – SiOMe 112 bottom up method 128 Bragg reflection 122, 162 Bragg reflector 220 Bragg-Brentano diffractometer 79 bubble 19 bulk isolation 33 bundling, atomic 112

C E-cage 129 capacitance relaxation 25 capture cross section 18, 21, 27 carbon nanotube device 232 carbon nanotube transistor 234 CARL, see lithography carrier lifetime 28 catadioptrics 162 CCD, see charge-coupled device CdS nanocluster 136 chabazite 129 channeling 57 charge carrier density 21, 89, 183 charge-coupled device 102, 103, 137 – buried channel 103 chemical shift 86, 131 chemical vapor deposition 44, 59, 121, 143 – chamber 45

262

Index

chromium mask 159 cluster 5, 14, 55, 109, 114 – Au55 cluster, ligand-stabilized 117 – SiC 8 – simulation of properties 5 – Sn 135 – SnO2 136 – xenon 163 cluster formation 109 colloidal dispersion 112 color center 13, 20, 162 conditioning 176 conduction band edge 15 conductivity 88 confinement 10, 12, 135 contact exposure 155 conversion coefficient 35 Coulomb blockade 104, 210, 226, 228 coupler, optoelectronic 34 CQUEST 160 crystal defect 13 crystal engineering 139 crystallinity 76 crystallite size 124 Cu 18 – clusters 138 – nanocomposites 113 – RHEED 82 current density 88, 90 cut and see 178, 186 CVD, see chemical vapor deposition cylinder capacitor 37 Czochralski – crystal 47 – silicon 19, 20, 30, 35

D DBQW, see double barrier quantum well De Broglie wavelength 5, 180 Debye-Scherrer formula 124 decomposition, thermal and ultrasonic 108 decoration 18 deep level transient spectroscopy 25 deep levels 52 deep UV 157 defect, see nanodefect – substitutional 17 defect engineering 37

depth of focus 157 developer 9 DFB QCL, see quantum cascade laser diamond 18, 143 – bandgap 8 – FIB sputtering 186 – nanopolishing 143 – non-diamond carbon phases 147 diaphragm 138 diborane (B2H6) 45, 85, 121 dielectric function 73 diffraction 5, 12, 76, 122, 125, 156, 169, 197 – electron 80 – x-ray 79, 125 diffractometer 79 diffusion 31, 51, 55, 113, 202 diode – Gunn 217 – light-emitting 34, 38 – MOS 25, 64, 91 – quantum 38 – resonant interband tunnel diode 215 – resonant tunneling 213, 218 – Schottky 25, 28 discharge, capillary 164 dislocation 18, 55, 79 dislocation loop 18 DLTS, see deep level transient spectroscopy donor, thermal 20, 30 – new 31 doping level 88 doping profile 92 doping properties 86 doping type 86 double barrier quantum well 213 double ring vibration 134 double vacancy 17, 55

E EBIC, see electron beam induced current ECR, see plasma etching e-gun 39, 40, 43, 48, 107 effusion cell 48 eigenenergy 6 eigenfunction 5 eigenvalue 5 electroluminescence 34, 224

Index electron, secondary 41, 178 electron beam induced current 101 electron beam lithography 114, 160, 164, 185 electron density 90 electron gun 39, 40, 43, 48, 107 electron spin resonance 20, 139 electrostatic storage 231 ellipsometry 69 – spectroscopic 73 emission time 27 emission time constant 26 energy gap 7 epitaxial layers 103 epitaxy 47 – heteroepitaxy 47, 109 – homoepitaxy 47 – liquid phase 47 – molecular beam 47 – solid state 47, 50 – vapor phase 45, 47 ESTOR, see electrostatic storage etching – chemical 34, 167, 172, 187 – dry 152 – in-situ 51 – ion etching, reactive 151, 153, 233 – nanostructures 150 – plasma etching 151 – progressive 153 EUV, see extreme ultraviolet – lithography 162, 172 evaporation 39, 48, 64, 227 exposure 155 – contact 155 – depth of focus 157 – EUV 161 – non-contact 156 – PREVAIL 167 – projection 157, 168 – resolution 157 – SCALPEL 166 extreme ultraviolet 161

F F2 laser 161 Fabry-Perot QCL 220 faujasite 130, 136, 140 FEA, see field emitter cathode array

263

Fermi-Dirac distribution 214 Fermi energy 182 Fermi level 21, 27 ferromagnetism 115 FET, see transistor FIB, see focused ion beams field effect, lateral 183 field emitter cathode array 233 filter, molecular 128, 138 fine structure constant 13 finesse 66 Fizeau strip 67 flat band point 95 flip-flop 217, 218 focused ion beams 160, 172 – accelerating mode 175 – annealing, thermal 179 – applications 181 – column 175 – cut and see 186 – decelerating mode 175 – doping by FIB 182 – equipment 173 – field effect, lateral 183 – isolation writing 182 – navigation of beam 177 – positive writing 183 – REM-FIB system 177 – resist lithography 185 – sample transfer 178 – sputtering 186 – stitching 177 focusing, electrostatic 180 forbidden band 25, 220 forbidden zone 12 forward resistance 29 Fourier transform infrared spectroscopy 100 four-probe measurement 88, 126 Frenkel defect 55 frequency shift 69 Fresnel – diffraction 169 – lens 187 – theory 72 FTIR, see Fourier transform infrared spectroscopy fullerene 6, 114, 118

264

Index

G GaAlAs 14, 50 gallium as LMIS 174 galliumimide 114 Gamess 7 GaN 18, 114, 228 gas chromatography 114 gas condensation 107 gate oxide thickness 202 Gaussian 7 generation current density 21 generation lifetime 21 generation rate 21 gettering zone 31 glass transition temperature 189 glow discharge 40 grinding 107 Gunn diode 217

H Hall constant 90 Hall effect 90 Hall mobility 90 Hamilton operator 5 HBT, see transistor heavy-ion accelerator 36 HEL, see lithography HEMT, see high electron mobility transistor heteroepitaxy 47, 109 high electron mobility transistor 179, 216 high frequency discharge 41 HIT, see solar cell hole density 90 homoepitaxy 47 hydrogen implantation 29 hydrogen plasma 19, 30, 37 Hyperchem 7

I ICP, see plasma etching IMPATT 216 implantation – in situ 50 – profile 55 – time 54

InAs, Auger spectrum 87 indium–tin–oxide 34, 103 infrared absorption 20, 22, 130, 134 injection laser 50 in-plane gate 183 interference colors 97 interference fringe 65 interferometer 65 interferometry 178 intrinsic density 27 ion beam lithography 168 ion bombardment 40 ion etching, reactive 151, 153, 233 ion implantation 34, 50, 52, 85 – single ion implantation 181 – system 53 ion milling 83 ion plating 39, 43 ion sputtering 107 IPG, see in-plane gate Irvin curves 89 isolation writing 182 ITO, see indium–tin–oxide

K Knudsen cell 48

L laser 14 – CO2 44 – excimer 44 – injection 50 – Nd:YAG 44 – quantum cascade, see quantum cascade laser – ruby 44 laser ablation 39, 44, 107 latent picture 102 Laue equation 78 layer – amorphous 126 – anti-reflection 103, 160 – thin 40 LBIC, see light beam induced current LDD doping 203 leakage current 29, 175

Index LEED, see low energy electron diffraction lens, calcium fluoride 162 leucite 129 light beam induced current 101 light-emitting diode 34, 38 line scan procedure 164 liquid metal ion source 173 liquid phase epitaxy 47 lithography 8, 154 – chemically amplified resist 160 – electron beam 114, 160, 164, 185 – EUV 161, 172 – hot embossing 189 – ion beam 168 – mold-assisted 191 – nanoimprint 189 – optical 155 – projection reduction exposure with variable axis immersion lenses (PREVAIL) 167 – resist lithography 185 – scattering with angular limitation projection electron beam (SCALPEL) 166 – soft 128, 195 – step and flash imprint 192 – synchrotron 169 – x-ray 169 LMIS, see liquid metal ion source Lorentz force 52, 89, 180 low energy electron diffraction 48, 80

265

millipede memory 231 mini-band 220 mini-gap 220 minimum to maximum capacitance 91 minority carrier lifetime 29 mix and match technique 185, 194 MMIC, see microwave integrated circuits mobility 88 MOCVD 211 MODFET 217 MOLCAO (molecular orbitals as linear combinations of atomic orbitals) 6 mold-assisted lithography 191 molecular beam epitaxy 47 moment development 57 monolayer, self-assembling 193 Monte-Carlo simulation 209 Moore’s law 2 Mopac 7 MOS capacitance 20, 26, 93 MOS diode 25, 64, 91 MOS oxide 34, 44 MOS profile measurement 93 MOS structure 13, 93, 209 MOS transistor 13, 64, 201 – low-temperature behavior 209 – sub-100 nm 204 MOS varactor 13 multi beam writer 166 multi column writer 166 multi wall nanotube 233 multiple beam interference 66

M Makyoh concept 102 mass spectrometer 83 Michelson interferometer 65 microbalance thermal analysis 138 microcontact printing 193 microscopy – atomic force 74, 128, 130, 195, 229, 231, 235 – high resolution electron 137 – scanning electron 130, 175 – scanning tunneling 74, 228 – transmission electron 130, 137, 187 microwave integrated circuits 217 microwave oscillator 215, 217 Miller indices 125

N nanocluster, see also cluster, 34, 116 – AsS 138 – CdS 136 – in zeolite host lattices 127, 135 – – applications 138 – – characterization 137 – – production 135 nanocomposite 113 nanodefect 17 – applications 28 – characterization 18 – forms 17 – generation 17 – nuclear track 35

266

Index

nanofilter 7 nanogear 7 nanoimprinting 188 nanolayer 39 – applications 103 – characterization 63 – production 39 nanoparticle 107, 135 – applications 117 – characterization 114 – Co nanoparticle 228 – fabrication 107 – GaN 114 nanopolishing of diamond 143 – characterization 144 nanotube 7 near-field optics 196 Neumann theory 72 nipi-superlattice 223 NMR spectroscopy 131 non-contact exposure 156 nuclear track, latent 36 nuclear tracks 35 numeric aperture 157

O off-axis illumination 160 oxidation – anodic 61 – dry 59 – thermal 59, 228 – wet 59 oxide capacitance 93 ozone 59

phase mask 159 – alternating chromium phase 159 – chromiumless 159 – half-tone 159 phase transition, congruent 49 phonon interaction 13 phosphine (PH3) 45, 121 photoluminescence 20, 34 photomask 156 photoresist 9, 73, 152, 154 physical vapor deposition 40 plasma, low-pressure and lowtemperature 109 plasma display, nanometric 36 plasma-enhanced chemical vapor deposition 121, 233 – system 46 plasma etching 151 – electron cyclotron resonance 153 – inductively coupled 153 platelet 19 PMMA, see polymethylmethacrylate point defect 29, 33 Poisson distribution 208 Poisson’s equation 95 polishing, thermochemical 143 polydimethylsiloxane 36, 193 polyethyleneterephthalate 36 polymethylmethacrylate 190 positive writing 183 potential well 12 powder, nanocrystalline 108 precipitation of quantum dots 113 PREVAIL, see lithography profilometer 73 projection exposure 157, 168 pulse curve 20

P PADOX technique 228, 232 pair formation 8 parallel plate reactor 150 paramagnetism 14 passivation layer 59 Pauli principle 6 PE, see plasma etching PECVD, see plasma-enhanced chemical vapor deposition PET, see polyethyleneterephthalate phase diagram of Ga and As 48

Q quantum cascade laser 219 – distributed feed back 222 – Fabry-Perot 220 quantum confinement effect 34 quantum diode 38 quantum dots 113, 219 – GaN 228 – precipitation 113 quantum size effect 138 quantum well 213

Index quantum well infrared photo detector 219, 224 quarter wave retarder 69 quartz crystal oscillator 69 QWIP, see quantum well infrared photo detector

R radiation defect 40 radio frequency – generator 41 – plasma 45 Raman shift 19 Raman spectroscopy 19, 130, 134, 138 rapid thermal annealing 85, 179, 203 reflection high energy electron diffraction 44, 82 refractive index 67, 69, 122 removal rate in thermochemical polishing 144 Rent’s rule 104 resist, organic 185 resistance, negative differential 214 resistivity 90, 104 resolution 11 resonant interband tunnel diode 215 resonant tunneling device 14 resonant tunneling diode 213, 218 reverse recovery 30 RHEED, see reflection high energy electron diffraction RIE, see ion etching RITD, see resonant interband tunnel diode RTA, see annealing Rutherford backscattering 96

S SAM, see monolayer SCALPEL, see lithography scanning tunneling microscopy 74, 228 scattering intensity 125 Schottky diode 25, 28 Schrödinger equation 5 secondary ion mass spectroscopy 48, 82 Seebeck effect 86

267

self-assembly 109 Semiconductor Industry Association 2 – Roadmap 2, 3 Shockley-Read-Hall generation recombination statistic 20, 22 SHT, see single hole transistor SIA roadmap 2, 3 SiC 18 SiC cluster 8 Si-H bonds 19 silane (SiH4) 45, 68, 109, 121 silicide 103 silicon – cathodoluminescence spectrum 115 – denuded 31 – nanocrystalline 121 – – applications 126 – – characterization 122 – – production 121 – porous 34 silicon gap 100 silicon-on-insulator 215, 226 silicon-on-oxide 33, 62 silicon-on-sapphire 33, 47 SIMS, see secondary ion mass spectroscopy single electron spectroscopy 229 single electron transistor 14, 225 single hole transistor 229 single wall nanotube 233 slow scan CCD system 137 smart cut 31, 37 Sn cluster 135 SnO2 cluster 136 sodalite cage 133, 136 soft cut 31, 37 SOI, see silicon-on-insulator sol gel 62, 112, 138 solar cell 37, 59 – heterojunction 126 – MIS 59 solid state epitaxy 47, 50 Soller slit 80 SOS, see silicon-on-sapphire space charge capacitance 93 space charge depth 22 space charge zone 95, 203 spacer width 203 spectroscopy – Auger 48, 86 – Fourier transform infrared 100

268

Index

– IR 134 – NMR 131 – photo-electron 8 – Raman 19, 130, 134, 138 – single electron 229 spray coating 154 spray gun 111 spraying, thermal high speed 110 spreading resistance 30 sputtering 40, 83 – capacitively coupled target 43 – gas-supported 187 standing wave 12, 111, 121 stencil mask 167 step and flash imprint lithography 192 step and repeat exposure 157 step scan exposure 158 STM, see scanning tunneling microscope Stranski-Krastanov growth 109 stretching band 114 storage of hydrogen 6, 139 storage time 28 striation 18 substrate 40 supercage 136 superlattice 81, 135, 220 superparamagnetism 115 supertip 173 surface reconstruction 80 SWNT, see single wall nanotube synchrotron lithography 169 synchrotron radiation 11

transferred electron device 217 transistor – bipolar 211 – carbon nanotube 234 – FET 216 – heterobipolar 216 – high electron mobility 179, 216 – MOS, see MOS transistor – MODFET 217 – single electron 225 – single hole 229 – TUBEFET 235 – velocity-modulated 183 transmission electron microscopy 130, 137, 187 transport theory 57 trap density 25 trimethylaluminum (Al[CH3]3) 203 trimethylborane (B[CH3]3) 121 TSI, see top surface imaging TUBEFET 235 tungsten hexacarbonyl (W[CO]6) 185 tunneling 13 tunneling current 14, 103, 195, 202, 225 two-probe measurement 89, 93

U UHV FIB 178 UV light 9

V T target 40 Taylor cone 174, 180 TED, see transferred electron device tetraethylorthosilicate 59 tetramethoxysilane 112 thermoelectric effect 86 third moment, standardized 58 threshold voltage 204, 207, 235 threshold voltage roll-off 204 TMOS, see tetramethoxysilane Tolanski method 66 top down method 128 top surface imaging 161 Townsend discharge 41

vacancy 6, 17, 55 valve, thermoresponsive 38 van der Pauw 91 van Wieringen 31 vapor deposition – chemical 44, 59, 121, 143 – physical 40 vapor phase epitaxy 45, 47 vector scan procedure 164 velocity, thermal 21, 27 velocity-modulated transistor 183 vibration mode 134 V-PADOX technique 228

Index

W wafer scan procedure 157 wagging band 114 Warmholz 31 wave function 12, 13, 15 Wien mass filter 181 work function 42, 209 work function engineering 209

X xenon cluster 163 xerogel 113 x-ray diffraction 79, 125, 130 x-ray powder diffractometry 138 x-ray topography 79 x-rays 11

Z zeolite 127 – adsorption 133 – characterization 130 – dehydrogenated 129 – high resolution electron microscopy 137 – ion exchange 130, 133 – IR spectroscopy 134 – nanoclusters 135 – NMR spectroscopy 131 – production 130 – scanning electron microscopy 131 – transmission electron microscopy 137 – x-ray spectroscopy 131 zeolite host lattice 135 zeolite modified electrode 138 zeolite-Y 136, 138 Zerbst plot 22

269

Printing: Strauss GmbH, Mörlenbach Binding: Schäffer, Grünstadt